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Mathematical method
analysis, a branch of mathematics, a selection theorem is a theorem that guarantees the existence of a single-valued selection function from a given set-valued
Selection_theorem
On convergent subsequences of functions that are locally of bounded total variation
In mathematics, Helly's selection theorem (also called the Helly selection principle) states that a uniformly bounded sequence of monotone real functions
Helly's_selection_theorem
On the existence of a continuous selection of a multivalued map from a paracompact space
Michael selection theorem is a selection theorem named after Ernest Michael. In its most popular form, it states the following: Michael Selection Theorem—Let
Michael_selection_theorem
Compact embedding theorem concerning Sobolev spaces
Rellich–Kondrachov selection theorem, since one "selects" a convergent subsequence. (However, today the customary name is "compactness theorem", whereas "selection theorem"
Rellich–Kondrachov_theorem
measurable selection theorem is a result from measure theory that gives a sufficient condition for a set-valued function to have a measurable selection function
Kuratowski and Ryll-Nardzewski measurable selection theorem
Kuratowski_and_Ryll-Nardzewski_measurable_selection_theorem
Sequences of convex sets in a bounded set have convergent subsequences
The Blaschke selection theorem is a result in topology and convex geometry about sequences of convex sets. Specifically, given a sequence { K n } {\displaystyle
Blaschke_selection_theorem
On convergent subsequences of regulated functions
In mathematics, the Fraňková–Helly selection theorem is a generalisation of Helly's selection theorem for functions of bounded variation to the case of
Fraňková–Helly selection theorem
Fraňková–Helly_selection_theorem
Principle relating genetic variance to fitness
Fisher's fundamental theorem of natural selection is an idea about genetic variance in population genetics developed by the statistician and evolutionary
Fisher's fundamental theorem of natural selection
Fisher's_fundamental_theorem_of_natural_selection
Topics referred to by the same term
theorem can mean either Ryll-Nardzewski fixed-point theorem A theorem in Omega-categorical theory Kuratowski and Ryll-Nardzewski measurable selection
Ryll-Nardzewski_theorem
On when a family of real, continuous functions has a uniformly convergent subsequence
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence
Arzelà–Ascoli_theorem
theorem (logic) Diaconescu's theorem (mathematical logic) Easton's theorem (set theory) Erdős–Dushnik–Miller theorem (set theory) Erdős–Rado theorem (set
List_of_theorems
Semicontinuity for set-valued functions
selections (Michael selection theorem, Bressan–Colombo directionally continuous selection theorem, Fryszkowski decomposable map selection). Likewise, upper
Hemicontinuity
Austrian mathematician (1884–1943)
mathematician after whom Helly's theorem, Helly families, Helly's selection theorem, Helly metric, and the Helly–Bray theorem were named. Helly earned his
Eduard_Helly
Austrian mathematician (1885–1962)
vol. 3 ISBN 3889082033 Several theorems and mathematical concepts are named for Blaschke: Blaschke selection theorem – Sequences of convex sets in a
Wilhelm_Blaschke
Theorem about a certain class of control-flow graphs
programming language theory, the structured program theorem, generally called the Böhm–Jacopini theorem, states that a class of control-flow graphs (historically
Structured_program_theorem
Provides conditions for a parametric optimization problem to have continuous solutions
to do so. Envelope theorem Brouwer fixed point theorem Kakutani fixed point theorem for correspondences Michael selection theorem Ok, Efe (2007). Real
Maximum_theorem
Mathematical function
measurable selections is important in the theory of differential inclusions, optimal control, and mathematical economics. See Selection theorem. Nicolas
Choice_function
Function whose values are sets (mathematics)
continuous selections as stated in the Michael selection theorem, which provides another characterisation of paracompact spaces. Other selection theorems, like
Set-valued_function
Fixed-point theorem for set-valued functions
In mathematical analysis, the Kakutani fixed-point theorem is a fixed-point theorem for set-valued functions. It provides sufficient conditions for a set-valued
Kakutani_fixed-point_theorem
Polish mathematician and logician
subsets of metric spaces; the Kuratowski and Ryll-Nardzewski measurable selection theorem; Kuratowski's post-war works were mainly focused on three strands:
Kazimierz_Kuratowski
Equivalence of optimization problems
In computer science and optimization theory, the max-flow min-cut theorem states that in a flow network, the maximum amount of flow passing from the source
Max-flow_min-cut_theorem
Counterintuitive result in probability
The infinite monkey theorem states that a monkey hitting keys independently and at random on a typewriter keyboard for an infinite amount of time will
Infinite_monkey_theorem
as the Arkhangel'skii–Frolík covering theorem and the Kuratowski and Ryll-Nardzewski measurable selection theorem. Baire space Stone–Čech compactification
Namioka's_theorem
Topics referred to by the same term
is paracompact. Michael selection theorem. This disambiguation page lists articles associated with the title Michael's theorem. If an internal link incorrectly
Michael's_theorem
Polish mathematician (1926–2015)
in model theory, and the Kuratowski and Ryll-Nardzewski measurable selection theorem. He became a member of the Polish Academy of Sciences in 1967. He
Czesław_Ryll-Nardzewski
Unsolved geometry problem
line segment (with translations allowed, but not rotations) Blaschke selection theorem, which can be used to prove that Lebesgue's universal covering problem
Lebesgue's universal covering problem
Lebesgue's_universal_covering_problem
Unsolved geometry problem about planar regions
a smallest convex cover. Its existence follows from the Blaschke selection theorem. It is also not trivial to determine whether a given shape forms a
Moser's_worm_problem
Theorem in functional analysis
and related branches of mathematics, the Banach–Alaoglu theorem (also known as Alaoglu's theorem) states that the closed unit ball of the dual space of
Banach–Alaoglu_theorem
On a property of surjective continuous maps between compact metric spaces
theorem Section 4 of Parthasarathy (1967). Page 12 of Fabec (2000) Baggett, Lawrence W. (1990), "A Functional Analytical Proof of a Borel Selection Theorem"
Federer–Morse_theorem
fundamental theorem is a theorem which is considered to be central and conceptually important for some topic. For example, the fundamental theorem of calculus
List of theorems called fundamental
List_of_theorems_called_fundamental
By a compactness argument (or equivalently in this case Helly's selection theorem for Stieltjes integrals), a subsequence of these probability measures
Positive_harmonic_function
Characterizes sets of lattices that are bounded in a certain sense
shorter vectors. It is also called his selection theorem, following an older convention used in naming compactness theorems, because they were formulated in
Mahler's_compactness_theorem
Fundamental theorem in probability theory and statistics
In probability theory, the central limit theorem (CLT) states that, under appropriate conditions, the distribution of a normalized version of the sample
Central_limit_theorem
Mathematical theorem in the study of analysis
In mathematical analysis, the Weierstrass approximation theorem states that every continuous function defined on a closed interval [a, b] can be uniformly
Stone–Weierstrass_theorem
Proof all ranked voting rules have spoilers
Arrow's impossibility theorem is a key result in social choice theory, proved by American economist Kenneth Arrow. It shows that no procedure for group
Arrow's_impossibility_theorem
Gives condition for a set of functions to be relatively compact in an Lp space
In functional analysis, the Fréchet–Kolmogorov theorem (the names of Riesz or Weil are sometimes added as well) gives a necessary and sufficient condition
Fréchet–Kolmogorov_theorem
Ecological theory concerning the selection of life history traits
The r/K selection theory is an evolutionary hypothesis examining the selection of traits in an organism that trade off between quantity and quality of
R/K_selection_theory
British mathematician and logician
contributions include the Spector–Gandy theorem, the Gandy Stage Comparison theorem, and the Gandy Selection theorem. He also made a significant contribution
Robin_Gandy
Non-empty convex set in Euclidean space
L+B^{n}(\epsilon ),L\subset K+B^{n}(\epsilon )\}.} Further, the Blaschke Selection Theorem says that every d-bounded sequence in K n {\displaystyle {\mathcal
Convex_body
Theorem in mathematics
In mathematical analysis, the inverse function theorem gives sufficient conditions for a function to have an inverse function. The essential idea is that
Inverse_function_theorem
quantum mechanics, the Landau–Yang theorem is a selection rule for particles that decay into two on-shell photons. The theorem states that a massive particle
Landau–Yang_theorem
Principle in genetics
Hardy–Weinberg principle, also known as the Hardy–Weinberg equilibrium, model, theorem, or law, states that allele and genotype frequencies in a population will
Hardy–Weinberg_principle
Topological space which is a generalization of certain compact spaces
metrization theorem) A topological space is metrizable if and only if it is paracompact, Hausdorff, and locally metrizable. Michael selection theorem states
Paracompact_space
Selective trading based on possession of hidden information
the latter case is the Myerson-Satterthwaite theorem. More recently, contract-theoretic adverse selection models have been tested both in laboratory experiments
Adverse_selection
Solution concept of a non-cooperative game
players. See also: Minimax theorem – Gives conditions that guarantee the max–min inequality holds with equality Equilibrium selection - explains how players
Nash_equilibrium
intersection theorem Kuratowski embedding Kuratowski–Ulam theorem Kuratowski-finite Kuratowski and Ryll-Nardzewski measurable selection theorem
List of things named after Kazimierz Kuratowski
List_of_things_named_after_Kazimierz_Kuratowski
Mathematical model of animal foraging behavior
natural selection results in animals utilizing the most economic and efficient strategy to balance energy gain and consumption. The marginal value theorem is
Marginal_value_theorem
Selection of decision-makers by random sample
In governance, sortition is the selection of public officials or jurors at random, i.e., by lottery, in order to obtain a representative sample. In ancient
Sortition
Weakly optimal allocation of resources
asymmetric information, signalling, adverse selection, and moral hazard are introduced, most people do not take the theorems of welfare economics as accurate descriptions
Pareto_efficiency
2023 film
Marguerite's Theorem (French: Le Théorème de Marguerite) is 2023 French-Swiss drama film co-written and directed by Anna Novion [fr]. It is about a female
Marguerite's_Theorem
Facilitating a peaceful outcome to a dispute
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Conflict_resolution
American mathematician
is credited with developing the theory of continuous selections. The Michael selection theorem is named for him, which he proved in (Michael 1956). Michael
Ernest_Michael
Pairing where no unchosen pair prefers each other over their choice
and hybrid CPU–GPU execution to reduce overhead. The rural hospitals theorem concerns a more general variant of the stable matching problem, like that
Stable_matching_problem
Number divisible only by 1 and itself
than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself
Prime_number
Mathematical models of strategic interactions
von Neumann. Von Neumann's original proof used the Brouwer fixed-point theorem on continuous mappings into compact convex sets, which became a standard
Game_theory
Logical paradox in decision-making theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Paradox_of_tolerance
space, then Reg([0, T]; X) satisfies a compactness theorem known as the Fraňková–Helly selection theorem. The set of discontinuities of a regulated function
Regulated_function
Theorem in game theory
Aumann's agreement theorem states that two Bayesian agents with the same prior beliefs cannot "agree to disagree" about the probability of an event if
Aumann's_agreement_theorem
English saying meaning "equivalent retaliation"
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Tit_for_tat
Military strategy during the Cold War with regard to the use of nuclear weapons
e12350. doi:10.1111/dome.12350. ISSN 1949-3606. Fearon, James (2002). "Selection Effects and Deterrence". International Interactions. 28 (1): 5–29. doi:10
Deterrence_theory
Israeli-American psychologist and economist (1934–2024)
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Daniel_Kahneman
Standard example in game theory
Abilene paradox Centipede game Collective action problem Externality Folk theorem (game theory) Free-rider problem Gift-exchange game Hobbesian trap Innocent
Prisoner's_dilemma
On decimal expansions of fractions with prime denominator and even repeat period
In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime
Midy's_theorem
Israeli psychologist (1937–1996)
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Amos_Tversky
Decision rule used for minimizing the possible loss for a worst-case scenario
important in the theory of repeated games. One of the central theorems in this theory, the folk theorem, relies on the minimax values. In combinatorial game theory
Minimax
Hungarian and American mathematician and physicist (1903–1957)
the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter unitary groups t → V t {\displaystyle
John_von_Neumann
Search algorithm
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Alpha–beta_pruning
Concept in game theory
Coordination game Simultaneous game Surprisingly popular Equilibrium selection Rendezvous problem, the mathematical problem of maximising the probability
Focal_point_(game_theory)
Theorem in mathematics and economics
In mathematics and economics, the envelope theorem is a major result about the differentiability properties of the value function of a parameterized optimization
Envelope_theorem
Class of theorems about Nash equilibrium payoff profiles in repeated games
In game theory, folk theorems are a class of theorems describing an abundance of Nash equilibrium payoff profiles in repeated games (Friedman 1971). The
Folk_theorem_(game_theory)
Application of game theory to evolving populations in biology
distribution. The distribution (an ESS) can be computed using the Bishop-Cannings theorem, which holds true for any mixed-strategy ESS. The distribution function
Evolutionary_game_theory
In board games that cannot end in a draw, one of the two players has a winning strategy
In game theory, Zermelo's theorem is a theorem about finite two-person games of perfect information in which the players move alternately and in which
Zermelo's theorem (game theory)
Zermelo's_theorem_(game_theory)
Overuse of a shared resource
environmental conditions, they mostly are filtered out (die) by environmental selection; hence, populations in hostile conditions are selected to be cooperative
Tragedy_of_the_commons
σ-finite measure, but the converse is again not true. Helly's selection theorem Helly–Bray theorem Klenke, Achim (2008). Probability Theory. Berlin: Springer
Sub-probability_measure
Statistical theorem
In statistics, Wilks' theorem offers an asymptotic distribution of the log-likelihood ratio statistic, which can be used to produce confidence intervals
Wilks'_theorem
Field of economics and game theory
described by Noam Nisan as a way to escape the Gibbard–Satterthwaite theorem. While the theorem is traditionally presented as a result about voting systems, it
Mechanism_design
Real function with finite total variation
Caccioppoli Caccioppoli set Lamberto Cesari Ennio De Giorgi Helly's selection theorem Locally integrable function Lp(Ω) space Lebesgue–Stieltjes integral
Bounded_variation
Situation where total gains match total losses
non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium
Zero-sum_game
Paper-and-pencil game for two players
successful landing and must be careful not to block themself. Hales–Jewett theorem m,n,k-game Number Scrabble Garcia, Dan. "GamesCrafters: Tic-Tac-Toe". gamescrafters
Tic-tac-toe
Concept in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Shapley_value
Model of conflict for two players in game theory
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Chicken_(game)
Combinatorial game theory theorem
In combinatorial game theory, the Sprague–Grundy theorem states that every impartial game under the normal play convention is equivalent to a one-heap
Sprague–Grundy_theorem
Hand game for two players or more
settle a dispute or make an unbiased group decision. Unlike truly random selection methods, however, rock paper scissors can be played with some degree of
Rock_paper_scissors
Model of humans as rational, self-interested agents
greatly exceeded that of the WTP. This was seen as falsifying the Coase theorem in which for every person the WTA equals the WTP that is the basis of the
Homo_economicus
Making of satisfactory, not optimal, decisions
incompatibility (help) Simon, Herbert (1990). "A mechanism for social selection and successful altruism". Science. 250 (4988): 1665–8. Bibcode:1990Sci
Bounded_rationality
Hand game for two or more players
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Chopsticks_(hand_game)
Russian-British scientist (1952–2025)
Markov ordering approach, Entropy 12(5) (2010), 1145–1193. A.N.Gorban. Selection Theorem for Systems With Inheritance. Math. Model. Nat. Phenom. Vol. 2, No
Alexander_Gorban
Game whose outcome can be correctly predicted
Computer Go Computer Othello Game complexity God's algorithm Zermelo's theorem (game theory) Allis, L.V. (1994). Searching for solutions in games and
Solved_game
Series of scientific papers by J. B. S. Haldane
A Mathematical Theory of Natural and Artificial Selection is the title of a series of scientific papers by the British population geneticist J.B.S. Haldane
A Mathematical Theory of Natural and Artificial Selection
A_Mathematical_Theory_of_Natural_and_Artificial_Selection
Human behavior pattern in which the participant takes on increasing risk
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Escalation_of_commitment
Probability theory paradox
is longer than a side of the inscribed triangle is 1/4. These three selection methods differ as to the weight they give to chords which are diameters
Bertrand paradox (probability)
Bertrand_paradox_(probability)
Theory and paradigm of statistics
Bayesian statistical methods use Bayes' theorem to compute and update probabilities after obtaining new data. Bayes' theorem describes the conditional probability
Bayesian_statistics
Conflict between safety and cooperation
attrition Theorems Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite
Stag_hunt
Ryll-Nardzewski fixed-point theorem. Schauder Schauder basis. Schatten Schatten class selection Michael selection theorem. self-adjoint A self-adjoint
Glossary of functional analysis
Glossary_of_functional_analysis
Description of how a trait or gene changes in frequency over time
the theory of evolution and natural selection, the Price equation (also known as Price's equation or Price's theorem) describes how a "characteristic" of
Price_equation
Primality test for numbers of a certain form
In number theory, Proth's theorem is a theorem which forms the basis of a primality test for Proth numbers known as Proth's test. Proth numbers, sometimes
Proth's_theorem
Counting polynomial roots in an interval
derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of p located in an interval
Sturm's_theorem
Branch of game theory about two-player sequential games with perfect information
that a player who cannot move loses. In the 1930s, the Sprague–Grundy theorem showed that all impartial games are equivalent to heaps in Nim, thus showing
Combinatorial_game_theory
Concept in mathematical optimization
over the multipliers. The Karush–Kuhn–Tucker theorem is sometimes referred to as the saddle-point theorem. The KKT conditions were originally named after
Karush–Kuhn–Tucker_conditions
Concept in game theory
Equilibrium selection is a concept from game theory which seeks to address reasons for players of a game to select a certain equilibrium over another
Equilibrium_selection
SELECTION THEOREM
SELECTION THEOREM
Boy/Male
Assamese, Bengali, Indian, Tamil
To Choose; Selection
Boy/Male
Tamil
Reflection
Boy/Male
Indian
Reflection; Gnawing Reflection
Girl/Female
Arabic, Muslim
Adopting; Selecting
Boy/Male
Muslim
Choice, Preference, Selection
Girl/Female
Indian, Malayalam
Reflection
Boy/Male
Arabic, Hindu, Indian, Muslim
Election; Last Dream
Boy/Male
Arabic, Muslim, Sindhi
Selection; Choice
Boy/Male
Arabic, Muslim
Choice; Preference; Selection
Boy/Male
Arabic, Muslim
Selecting; Adopting
Boy/Male
Muslim/Islamic
Selection choice
Boy/Male
Tamil
Gunjik | கà¯à®¨à¯à®œà¯€à®•
Reflection
Gunjik | கà¯à®¨à¯à®œà¯€à®•
Girl/Female
Assamese, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Oriya, Tamil, Telugu
Reflection; Outlook; Reflection Reflection
Boy/Male
Hindu
Reflection
Boy/Male
Muslim
Selection, Choice
Girl/Female
Hindu, Indian
Reflection
Boy/Male
Vietnamese
Section.
Girl/Female
American, Hindu, Indian
Selection
Boy/Male
Hindu
Reflection
Girl/Female
Japanese
Mirror reflection.
SELECTION THEOREM
SELECTION THEOREM
Girl/Female
Indian
Happy Friend
Boy/Male
Arabic
Just King
Girl/Female
Hebrew Arabic Muslim Greek Irish Welsh
Fire.
Girl/Female
Indian, Tamil
Melody; Music
Girl/Female
Australian, British, Christian, Dutch, English, French, German, Netherlands, Swedish
Form of Charlotte; Petite and Feminine; Female Version of Charles; Carl; Little and Womanly; Free Man
Girl/Female
Indian
The Flower Jasmine
Girl/Female
Irish
From the Greek Cleone: daughter of a river god.
Girl/Female
Algerian, Arabic, Australian, Danish, Hebrew, Russian
Short Form of Lover
Girl/Female
Arabic, Latin, Muslim
Divine; God Like
Boy/Male
Tamil
Lankineebhanjana | லாநà¯à®•à¯€à®¨à¯€à®ªà®¾à®¨à¯à®œà®¾à®¨à®¾
Slayer of lankini
SELECTION THEOREM
SELECTION THEOREM
SELECTION THEOREM
SELECTION THEOREM
SELECTION THEOREM
a.
Selecting; tending to select.
n.
A part reflected, or turned back, at an angle; as, the reflection of a membrane.
adv.
With care and selection.
n.
An election held by itself, not at the time of a general election.
n.
Election beforehand.
n.
That which is selected; a collection of things chosen; as, a choice selection of books.
n.
A projecting molding round a panel. Same as Bilection.
n.
The act of cutting, or separation by cutting; as, the section of bodies.
a.
The act of choosing; choice; selection.
n.
That which is produced by reflection.
n.
A lesson or selection, esp. of Scripture, read in divine service.
n.
The act of selecting, or the state of being selected; choice, by preference.
n.
The return of rays, beams, sound, or the like, from a surface. See Angle of reflection, below.
n.
That portion of a group of moldings which projects beyond the general surface of a panel; a bolection.
n.
Election a second time, or anew; as, the reelection of a former chief.
n.
The act of detecting; the laying open what was concealed or hidden; discovery; as, the detection of a thief; the detection of fraud, forgery, or a plot.
a.
The act of choosing a person to fill an office, or to membership in a society, as by ballot, uplifted hands, or viva voce; as, the election of a president or a mayor.
pl.
of Selectman
n.
Casual choice; fortuitous selection; hazard.
n.
Selection or appointment by lot.