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Concept in probability theory
probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes plays
Markov_kernel
Category whose objects are measurable spaces and whose morphisms are Markov kernels
category of Markov kernels, often denoted Stoch, is the category whose objects are measurable spaces and whose morphisms are Markov kernels. It is analogous
Category_of_Markov_kernels
{\mathcal {F}},\mathbb {P} )} is called a time homogeneous Markov chain with Markov kernel p {\displaystyle p} and start distribution μ {\displaystyle
Markov chains on a measurable state space
Markov_chains_on_a_measurable_state_space
Deep learning method
{\displaystyle \Omega } . The discriminator's strategy set is the set of Markov kernels μ D : Ω → P [ 0 , 1 ] {\displaystyle \mu _{D}:\Omega \to {\mathcal {P}}[0
Generative adversarial network
Generative_adversarial_network
Mathematical function
measures or stochastic processes. The most important example of kernels are the Markov kernels. Let ( S , S ) {\displaystyle (S,{\mathcal {S}})} , ( T , T
Transition_kernel
the Markov operator admits a kernel representation. Markov operators can be linear or non-linear. Closely related to Markov operators is the Markov semigroup
Markov_operator
Random process independent of past history
In probability theory and statistics, a Markov chain or Markov process is a stochastic process describing a sequence of possible events in which the probability
Markov_chain
Hierarchical hidden Markov model Maximum-entropy Markov model Variable-order Markov model Markov renewal process Markov chain mixing time Markov kernel Piecewise-deterministic
List of things named after Andrey Markov
List_of_things_named_after_Andrey_Markov
Abstract structure modeling spaces of probability measures
probability measures which depend measurably on a parameter (giving rise to Markov kernels), or when one has probability measures over probability measures (such
Giry_monad
Equation from probability theory
the Markov kernels induced by the transitions of a Markov process, the Chapman-Kolmogorov equation can be seen as giving a way of composing the kernel, generalizing
Chapman–Kolmogorov_equation
Calculation of complex statistical distributions
{X}},{\mathcal {B}}({\mathcal {X}}))} , the Markov chain ( X n ) {\displaystyle (X_{n})} with transition kernel K ( x , y ) {\displaystyle K(x,y)} is φ-irreducible
Markov_chain_Monte_Carlo
Matrix used to describe the transitions of a Markov chain
stochastic matrix is a square matrix used to describe the transitions of a Markov chain. Each of its entries is a nonnegative real number representing a probability
Stochastic_matrix
Conditional independence of exchangeable observations
permutation action on X N {\displaystyle X^{\mathbb {N} }} , as well as the Markov kernel X N → X N {\displaystyle X^{\mathbb {N} }\to X^{\mathbb {N} }} induced
De_Finetti's_theorem
Concept in probability theory
distribution is a parametrized family of probability measures called a Markov kernel. Consider two random variables X , Y : Ω → R {\displaystyle X,Y:\Omega
Regular conditional probability
Regular_conditional_probability
theory are The category of measurable spaces; Markov categories such as the category of Markov kernels; Probability monads such as Giry monad. W. Lawvere
Categorical_probability
Overview of and topical guide to machine learning
LogitBoost Manifold alignment Markov chain Monte Carlo (MCMC) Minimum redundancy feature selection Mixture of experts Multiple kernel learning Naive Bayes classifier
Outline_of_machine_learning
Category whose objects are measurable spaces and whose morphisms are measurable maps
measure spaces Category of Markov kernels – Category whose objects are measurable spaces and whose morphisms are Markov kernels Measurable space – Basic
Category_of_measurable_spaces
Class of algorithms for pattern analysis
In machine learning, kernel machines are a class of algorithms for pattern analysis, whose best known member is the support-vector machine (SVM). These
Kernel_method
Expected value of a random variable given that certain conditions are known to occur
(1_{X\in B}|{\mathcal {H}})(\omega ).} It can be shown that they form a Markov kernel, that is, for almost all ω {\displaystyle \omega } , κ H ( ω , − ) {\displaystyle
Conditional_expectation
In statistical classification, the Fisher kernel, named after Ronald Fisher, is a function that measures the similarity of two objects on the basis of
Fisher_kernel
Stochastic way of assigning quantities across a space
processes there is the related concept of a stochastic kernel, probability kernel, Markov kernel. Define M ~ := { μ ∣ μ is measure on ( E , E ) } {\displaystyle
Random_measure
process Markov information source Markov kernel Markov logic network Markov model Markov network Markov process Markov property Markov random field Markov renewal
List_of_statistics_articles
Examples of the probabilistic construct
contains examples of Markov chains and Markov processes in action. All examples are in the countable state space. For an overview of Markov chains in general
Examples_of_Markov_chains
Sigma-algebra used in probability and ergodic theory
{\displaystyle 1_{T^{-1}(S)}} . Similarly, given a measure-preserving Markov kernel k : ( X , F , p ) → ( X , F , p ) {\displaystyle k:(X,{\mathcal {F}}
Invariant_sigma-algebra
Probability theorem
^{i-1},{\mathcal {A}}^{i-1})\to (\Omega _{i},{\mathcal {A}}_{i})} be the Markov kernel derived from ( Ω i − 1 , A i − 1 ) {\displaystyle (\Omega ^{i-1},{\mathcal
Ionescu-Tulcea_theorem
Lossless compression algorithm
LZMA (Lempel–Ziv–Markov chain algorithm) is a lossless data compression algorithm developed since 1998 by Igor Pavlov, the developer of 7-Zip. It has been
LZMA
1968 book by Robert M. Blumenthal and Ronald K. Getoor
processes and potential theory Chapter I covers the Markov property and strong Markov property, Markov kernels, standard and Hunt processes, and measurability
Markov Processes and Potential Theory
Markov_Processes_and_Potential_Theory
Principle in kinetic systems
balance in kinetics seem to be clear. A Markov process is called a reversible Markov process or reversible Markov chain if there exists a positive stationary
Detailed_balance
Graphical representation of a morphism
Artificial neural networks Game theory Bayesian probability Consciousness Markov kernels Signal-flow graphs Conjunctive queries Bidirectional transformations
String_diagram
probability kernels { Λ n } n = 1 N {\displaystyle \{\Lambda ^{n}\}_{n=1}^{N}} such that θ k 1 {\displaystyle \theta _{k}^{1}} is a Markov chain with transition
Telescoping_Markov_chain
Mathematical object that generalizes the standard notions of sets and functions
category. If all morphisms have a kernel and a cokernel, and all epimorphisms are cokernels and all monomorphisms are kernels, then we speak of an abelian
Category_(mathematics)
Concept in probability theory
} . A superprocess has a number of properties. It is a Markov process, and its Markov kernel Q t ( μ , d ν ) {\displaystyle Q_{t}(\mu ,d\nu )} verifies
Superprocess
Markov additive process Markov blanket / Bay Markov chain mixing time / (L:D) Markov decision process Markov information source Markov kernel Markov logic
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Machine learning software library in C++
kernel machines such as support vector machines for regression and classification problems. Shogun also offers a full implementation of Hidden Markov
Shogun_(toolbox)
Set of methods for supervised statistical learning
using the kernel trick, representing the data only through a set of pairwise similarity comparisons between the original data points using a kernel function
Support_vector_machine
Class of nonparametric methods
In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which
Kernel embedding of distributions
Kernel_embedding_of_distributions
Topics referred to by the same term
a protein fragment Heterogeneous memory management, in the Linux kernel Hidden Markov model, a statistical model Central Mashan Miao language (ISO 639-3
HMM
Tree-based ensemble machine learning methods
adaptive kernel estimates. Davies and Ghahramani proposed Kernel Random Forest (KeRF) and showed that it can empirically outperform state-of-art kernel methods
Random_forest
Statistical model
Bayesian interpretation of regularization Kriging Gaussian free field Gauss–Markov process Gradient-enhanced kriging (GEK) Student's t-process MacKay, David
Gaussian_process
Field of machine learning
knowledge of an exact mathematical model of the Markov decision process, and they target large Markov decision processes where exact methods become infeasible
Reinforcement_learning
Projection of data onto lower-dimensional manifolds
that the kernel captures some local geometry of data set. The Markov chain defines fast and slow directions of propagation through the kernel values. As
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
Type of stochastic Markov process
x] ≥ ερ(c) for all x ∈ A and all c ∈ Ω. Let {Xn}, Xn ∈ Rd be a Markov chain with a kernel that is absolutely continuous with respect to Lebesgue measure:
Harris_chain
B} in S {\displaystyle S} . Further, let ν {\displaystyle \nu } be a Markov kernel from S {\displaystyle S} to T {\displaystyle T} . Let τ k {\displaystyle
Nu-transform
Geometric algorithm
Diffusion maps exploit the relationship between heat diffusion and random walk Markov chain. The basic observation is that if we take a random walk on the data
Diffusion_map
In machine learning, the kernel perceptron is a variant of the popular perceptron learning algorithm that can learn kernel machines, i.e. non-linear classifiers
Kernel_perceptron
Generalized function whose value is zero everywhere except at zero
is then an expression of the Markov property of Brownian motion. In higher-dimensional Euclidean space Rn, the heat kernel is η ε = 1 ( 2 π ε ) n / 2 e
Dirac_delta_function
Simulation method in statistics
user-defined reversible jump MCMC kernels as part of its Involution MCMC feature. Green, P.J. (1995). "Reversible Jump Markov Chain Monte Carlo Computation
Reversible-jump Markov chain Monte Carlo
Reversible-jump_Markov_chain_Monte_Carlo
Interface between statistics and computer science
statistical methods including resampling methods, Markov chain Monte Carlo methods, local regression, kernel density estimation, artificial neural networks
Computational_statistics
Equation that describes density changes of a material that is diffusing in a medium
particles (see Fick's laws of diffusion). In mathematics, it is related to Markov processes, such as random walks, and applied in many other fields, such
Diffusion_equation
Markov processes by establishing a precise link, in a very general framework, between an important class of Markov processes and the class of kernels
Hunt_process
German computer scientist
computer scientist known for his work in machine learning, especially on kernel methods and causality. He is a director at the Max Planck Institute for
Bernhard_Schölkopf
Mathematical measure space associated to a random walk
{\displaystyle \partial \mathbb {D} } as the space of trajectories for a Markov process is a special case of the construction of the Poisson boundary. Finally
Poisson_boundary
Mathematical form
{R} ^{n}\to \mathbb {R} } is some non-negative symmetric integral kernel. If the kernel k {\displaystyle k} satisfies the bound k ( x , y ) ≤ Λ | x − y
Dirichlet_form
Mathematical technique
method, and we start with an initial estimate x {\displaystyle x} . Let a kernel function K ( x i − x ) {\displaystyle K(x_{i}-x)} be given. This function
Mean_shift
Neural network technology
small window (called a kernel or filter) across the input data and computing the dot product between the values in the kernel and the input at each position
Convolutional_layer
Stochastic matrix representing links between entities
matrix of links. A related matrix S corresponding to the transitions in a Markov chain of given network is constructed from A by dividing the elements of
Google_matrix
Type of feedforward neural network
type of feedforward neural network that learns features via filter (or kernel) optimization. This type of deep learning network has been applied to process
Convolutional_neural_network
Process forming a path from many random steps
+ b ) {\displaystyle O(a+b)} in the general one-dimensional random walk Markov chain. Some of the results mentioned above can be derived from properties
Random_walk
British mathematician
of the Cambridge Centre for Analysis. Norris, J. R. (28 February 1997). Markov Chains. Cambridge University Press. doi:10.1017/cbo9780511810633. ISBN 978-0-521-48181-6
James_R._Norris
Set of machine learning methods
Multiple kernel learning refers to a set of machine learning methods that use a predefined set of kernels and learn an optimal linear or non-linear combination
Multiple_kernel_learning
in time. The Wiener-Hopf factorization gives the transition probability kernel in the discrete time case. Record value Asmussen, S. R. (2003). "Random
Ladder_height_process
Type of random number generator
software running on a general-purpose computer. NPTRNGs are found in the kernels of popular operating systems that are expected to run on any generic CPU
Non-physical true random number generator
Non-physical_true_random_number_generator
Automated recognition of patterns and regularities in data
analysis (PCA) Conditional random fields (CRFs) Hidden Markov models (HMMs) Maximum entropy Markov models (MEMMs) Recurrent neural networks (RNNs) Dynamic
Pattern_recognition
Statistical formula
Stein's method. It was first formulated as a tool to assess the quality of Markov chain Monte Carlo samplers, but has since been used in diverse settings
Stein_discrepancy
Software projects developed at universities
language processing and text-mining framework (Sheffield) HTK – hidden Markov model toolkit for speech recognition (Cambridge) Kaldi – speech recognition
List of software developed at universities
List_of_software_developed_at_universities
Model-free reinforcement learning algorithm
improving this choice by trying both directions over time. For any finite Markov decision process, Q-learning finds an optimal policy in the sense of maximizing
Q-learning
Game where groups of players may enforce cooperative behaviour
the nucleolus is in the core. The nucleolus is always in the kernel, and since the kernel is contained in the bargaining set, it is always in the bargaining
Cooperative_game_theory
outlier factor Logic learning machine LogitBoost LPBoost Manifold alignment Markov chain Monte Carlo (MCMC) Minimum redundancy feature selection Naive Bayes
List of artificial intelligence algorithms
List_of_artificial_intelligence_algorithms
Type of database that uses vectors to represent other data
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Vector_database
Japanese mathematician (born 1935)
Ito's theory of stochastic integration, initially developed by Ito for Markov processes, to square integrable martingales. This theory, known as the Kunita-Watanabe
Shinzo_Watanabe
Overview of and topical guide to statistics
Lasso (statistics) Survival analysis Density estimation Kernel density estimation Multivariate kernel density estimation Time series Time series analysis
Outline_of_statistics
Class of statistical modeling methods
{Y}}_{v}} , conditioned on X {\displaystyle {\boldsymbol {X}}} , obeys the Markov property with respect to the graph; that is, its probability is dependent
Conditional_random_field
Algorithm that estimates unknowns from a series of measurements over time
be an unobserved Markov process, and the measurements are the observed states of a hidden Markov model (HMM). Because of the Markov assumption, the true
Kalman_filter
Method of machine learning
independent of training data size). For many formulations, for example nonlinear kernel methods, true online learning is not possible, though a form of hybrid online
Online_machine_learning
Concept in regression analysis mathematics
notation, the i , j {\displaystyle i,j} entry of kernel matrix K {\displaystyle K} (as opposed to kernel function K ( ⋅ , ⋅ ) {\displaystyle K(\cdot ,\cdot
Regularized_least_squares
convex optimization. Where the steps can be modelled as a Markov chain, then Hidden Markov Models are also often used (a popular approach in the biophysics
Step_detection
Type of large language model
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Generative pre-trained transformer
Generative_pre-trained_transformer
Type of feedforward neural network
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Multilayer_perceptron
Cryptographic hash function
reasons I care is for the kernel, we had a break in on one of the BitKeeper sites where people tried to corrupt the kernel source code repositories. However
SHA-1
Type of machine learning model
determination Confusion matrix Learning curve ROC curve Mathematical foundations Kernel machines Bias–variance tradeoff Computational learning theory Empirical
Large_language_model
Influential 2012 deep convolutional neural network
S2CID 2161592. Taskar, Ben; Guestrin, Carlos; Koller, Daphne (2003). "Max-Margin Markov Networks". Advances in Neural Information Processing Systems. 16. MIT Press
AlexNet
Iterative method for finding maximum likelihood estimates in statistical models
{Z} } or through an algorithm such as the Viterbi algorithm for hidden Markov models. Conversely, if we know the value of the latent variables Z {\displaystyle
Expectation–maximization algorithm
Expectation–maximization_algorithm
Dividing things between two categories
other kernel-based learning methods. Cambridge University Press, 2000. ISBN 0-521-78019-5 ([1] SVM Book) John Shawe-Taylor and Nello Cristianini. Kernel Methods
Binary_classification
Statistical technique
of the data. Underlying model: Following centering, the standard Gauss–Markov linear regression model for Y {\displaystyle \mathbf {Y} } on X {\displaystyle
Principal component regression
Principal_component_regression
Technique for the generative modeling of a continuous probability distribution
efficiency and quality. There are various equivalent formalisms, including Markov chains, denoising diffusion probabilistic models, noise conditioned score
Diffusion_model
Similarity measure for number sequences
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Cosine_similarity
Machine learning technique
{\mathcal {T}}_{S}} . Algorithms for transfer learning are available in Markov logic networks and Bayesian networks. Transfer learning has been applied
Transfer_learning
Canadian statistician
Matrix In Monte Carlo Sampling Methods Using Markov Chains" developed the Peskun ordering on Markov chain kernels. In 1971, Hastings joined the department
W._K._Hastings
Quantum algorithm for integer factorization
group homomorphism. The kernel corresponds to the multiples of ( r , 1 ) {\displaystyle (r,1)} . So, if we can find the kernel, we can find r {\displaystyle
Shor's_algorithm
Sequence of data points over time
See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution. A hidden Markov model (HMM) is a statistical Markov model in
Time_series
Machine learning technique
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Reinforcement learning from human feedback
Reinforcement_learning_from_human_feedback
Conversational software
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Chatbot
Deep learning architecture
algorithm enables efficient computation on modern hardware, like GPUs, by using kernel fusion, parallel scan, and recomputation. The implementation avoids materializing
Mamba (deep learning architecture)
Mamba_(deep_learning_architecture)
Reverse-engineering neural networks
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov Anomaly detection RANSAC k-NN Local outlier factor Isolation forest Neural
Mechanistic_interpretability
Intelligence of machines
evaluate situations while being uncertain of what the outcome will be. A Markov decision process has a transition model that describes the probability that
Artificial_intelligence
Resource problem in machine learning
independent Markov machine. Each time a particular arm is played, the state of that machine advances to a new one, chosen according to the Markov state evolution
Multi-armed_bandit
Category of regression analysis
Bayes. The hyperparameters typically specify a prior covariance kernel. In case the kernel should also be inferred nonparametrically from the data, the critical
Nonparametric_regression
trees Gaussian Mixture Models (GMMs) Hidden Markov Models (HMMs) Kernel density estimation (KDE) Kernel Principal Component Analysis (KPCA) K-Means Clustering
Mlpack
Machine learning technique
(\mathbf {x} ',\mathbf {x} _{j})} where φ {\displaystyle \varphi } is the kernel function (usually Gaussian), α j {\displaystyle \alpha _{j}} are the variances
Relevance_vector_machine
Approach in data analysis
autoencoders, long short-term memory neural networks Bayesian networks Hidden Markov models (HMMs) Minimum Covariance Determinant Deep Learning Convolutional
Anomaly_detection
MARKOV KERNEL
MARKOV KERNEL
Surname or Lastname
English
English : from a pet form of the personal name Mary (Marie) or possibly sometimes from a pet form of the much less common male personal name Mark 1.Jewish (eastern Ashkenazic) : patronymic from the Yiddish personal name Marke, a variant of Mark.
Male
Italian
Italian and Spanish form of Latin Marius, MARIO means "male, virile."
Male
Greek
(ΜάÏκος) Greek form of Latin Marcus, MARKOS means "defense" or "of the sea." In the New Testament bible, this is the name of the author of the second Gospel.
Male
German
 German form of Latin Marcus, MARKUS means "defense" or "of the sea." Compare with another form of Markus.
Female
English
Pet form of French Marguerite, MARGOT means "pearl."
Surname or Lastname
English and Dutch
English and Dutch : patronymic from Mark 1.English : variant of Mark 2.German and Jewish (western Ashkenazic) : reduced form of Markus, German spelling of Marcus (see Mark 1).
Male
Hebrew
(יַעֲקׄב) Variant spelling of Hebrew Yaaqob, YAAKOV means "supplanter."Â
Male
Spanish
Portuguese and Spanish form of Latin Marcus, MARCOS means "defense" or "of the sea."
Boy/Male
Russian
Of Mars; the god of war.
Male
English
Probably an English contraction of French Marcelon, MARLON means "little one of the sea." This name was first brought to public attention by the American actor Marlon Brando whose family is said to be of French descent.Â
Male
German
 Serbian and Slovene form of Greek Markos, MARKO means "defense" or "of the sea." Also in use by the Basques, Bulgarians, Dutch, Finnish, Germans, and Romani. Compare with another form of Marko.
Female
Japanese
(真里å) Japanese name MARIKO means "true village child."
Female
English
English variant spelling of French Margot, MARGO means "pearl."
Male
Finnish
Finnish form of Greek Markos, MARKKU means "defense" or "of the sea."
Surname or Lastname
English and Jewish (Ashkenazic)
English and Jewish (Ashkenazic) : patronymic from the personal name Mark.
Surname or Lastname
English
English : variant spelling of Marks.
Male
English
 Pet form of English Mark, MARKO means "defense" or "of the sea." Compare with another form of Marko.
Surname or Lastname
English
English : topographic name for someone who lived by a market, Middle English market.
Female
Japanese
(舞å) Japanese name MAIKO means "dancing child."
Male
English
 English form of Latin Marcus, MARKUS means "defense" or "of the sea." Compare with another form of Markus.
MARKOV KERNEL
MARKOV KERNEL
Boy/Male
Arabic, Muslim, Sindhi
The Name of the Makes of Astrolabes
Male
English
Variant spelling of English Aidan, EDAN means "little fire."
Boy/Male
Arabic, Muslim
Desired
Boy/Male
Hindu
Month in Hindu calendar
Boy/Male
British, English
Weaver
Girl/Female
Hindu, Indian
Moon
Male
Welsh
Pet form of Welsh Aneirin, NYE means "modest, noble."Â
Boy/Male
German, Scottish
From the Stockade
Boy/Male
Tamil
Mythical vehicle of Lord Vishnu
Male
Egyptian
, the chief funereal priest.
MARKOV KERNEL
MARKOV KERNEL
MARKOV KERNEL
MARKOV KERNEL
MARKOV KERNEL
v. t.
To be a mark upon; to designate; to indicate; -- used literally and figuratively; as, this monument marks the spot where Wolfe died; his courage and energy marked him for a leader.
a.
A chestnut color; maroon.
n.
An explosive shell. See Marron, 3.
v. t.
To leave a trace, scratch, scar, or other mark, upon, or any evidence of action; as, a pencil marks paper; his hobnails marked the floor.
a.
Designated or distinguished by, or as by, a mark; hence; noticeable; conspicuous; as, a marked card; a marked coin; a marked instance.
n.
The soldier who forms the pilot of a wheeling column, or marks the direction of an alignment.
v. t.
To put a mark upon; to affix a significant mark to; to make recognizable by a mark; as, to mark a box or bale of merchandise; to mark clothing.
v. i.
To deal in a market; to buy or sell; to make bargains for provisions or goods.
imp. & p. p.
of Mark
v. t.
To expose for sale in a market; to traffic in; to sell in a market, and in an extended sense, to sell in any manner; as, most of the farmes have marketed their crops.
v. t.
To fill with, or as with, marrow of fat; to glut.
a.
Having the color called maroon. See 4th Maroon.
n.
The price for which a thing is sold in a market; market price. Hence: Value; worth.
a.
Having ripple marks.
n.
Exchange, or purchase and sale; traffic; as, a dull market; a slow market.
n.
One who or that which marks.
n.
A number or other character used in registring; as, examination marks; a mark for tardiness.
n.
A public place (as an open space in a town) or a large building, where a market is held; a market place or market house; esp., a place where provisions are sold.
n.
An opportunity for selling anything; demand, as shown by price offered or obtainable; a town, region, or country, where the demand exists; as, to find a market for one's wares; there is no market for woolen cloths in that region; India is a market for English goods.
n.
The privelege granted to a town of having a public market.