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Mathematical measure for topological spaces
In mathematics, a regular measure on a topological space is a measure for which every measurable set can be approximated from above by open measurable
Regular_measure
Type of mathematical measure
all compact sets, outer regular on all Borel sets, and inner regular on open sets. These conditions guarantee that the measure is "compatible" with the
Radon_measure
Type of measure on Euclidean spaces
In mathematics, an outer measure μ on n-dimensional Euclidean space Rn is called a Borel regular measure if the following two conditions hold: Every Borel
Borel_regular_measure
Topics referred to by the same term
Cauchy sequences Regular functions, functions that are analytic and single-valued (unique) in a given region Regular measure, a measure for which every
Regular
1986 studio album by Icehouse
Measure for Measure is the fourth studio album by the Australian rock band Icehouse, released in April 1986 in Australia by Regular Records and in the
Measure_for_Measure_(album)
Segment of time corresponding to a specific number of beats
hypermeasure, large-scale or high-level measure, or measure-group is a metric unit in which, generally, each regular measure is one beat (actually hyperbeat)
Bar_(music)
Generalization of mass, length, area and volume
measure Product measure Pushforward measure Random measure Regular measure Vector measure Valuation (measure theory) Volume form One way to rephrase our definition
Measure_(mathematics)
Left-invariant (or right-invariant) measure on locally compact topological group
all compact K ⊆ G {\displaystyle K\subseteq G} . The measure μ {\displaystyle \mu } is outer regular on Borel sets S ⊆ G {\displaystyle S\subseteq G} :
Haar_measure
Shape with equal angles and equal sides
regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons
Regular_polygon
Measure defined on all open sets of a topological space
equivalent. If a Borel measure μ {\displaystyle \mu } is both inner regular and outer regular, it is called a regular Borel measure. If μ {\displaystyle
Borel_measure
Mathematical function
In the mathematical field of measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the
Outer_measure
its radius and not on its centre. By convention, the measure is also required to be Borel regular, and to take positive and finite values on open balls
Uniformly_distributed_measure
Measure that is 1 if and only if a specified element is in the set
condition to be an inner regular measure, since singleton sets such as {x} are always compact. Hence, δx is also a Radon measure. Assuming that the topology
Dirac_measure
mathematics, a locally finite measure is a measure for which every point of the measure space has a neighbourhood of finite measure. Let ( X , T ) {\displaystyle
Locally_finite_measure
Fijian dance
Fijian poet is poetry with every verse ending with the same vowel of regular measure, which in practice is often achieved with poetic license through the
Meke
Concept in measure theory
{\displaystyle \mu } may either be said to be a tight measure or to be an inner regular measure. If Y {\displaystyle Y} is an X {\displaystyle X} -valued random variable
Tightness_of_measures
In measure theory, a branch of mathematics, a finite measure or totally finite measure is a special measure that always takes on finite values. Among finite
Finite_measure
Measure for Baire sets in mathematics
by regular Borel measures. The relation between Baire measures and regular Borel measures is as follows: The restriction of a finite Borel measure to
Baire_measure
Four-dimensional analogue of the cube
convex regular 4-polytopes. The tesseract is also called an 8-cell, C8, (regular) octachoron, or cubic prism. It is the four-dimensional measure polytope
Tesseract
Statement about linear functionals and measures
support, and the measures can be Baire measures or regular Borel measures or Radon measures or signed measures or complex measures. The statement of
Riesz–Markov–Kakutani representation theorem
Riesz–Markov–Kakutani_representation_theorem
Concept in probability theory
that it be regular, that is: For almost all x, A ↦ κ Y ∣ X ( x , A ) {\displaystyle A\mapsto \kappa _{Y\mid X}(x,A)} is a probability measure For all A
Regular conditional probability
Regular_conditional_probability
X is any metric space and μ is an inner regular (or tight) measure on X, then (X, BX, μ) is a perfect measure space, where BX denotes the Borel σ-algebra
Perfect_measure
In mathematics, a Rajchman measure, studied by Rajchman (1928), is a regular Borel measure on a locally compact group such as the circle, whose Fourier
Rajchman_measure
ballot measures on the general election ballot. As a result of the election, two passed and three were rejected by voters. Oregon Ballot Measure 115, entitled
2024_Oregon_elections
Tool used to physically measure lengths
they can also be flat boards. Some have markings at regular intervals. It is likely that the measuring rod was used before the line, chain or steel tapes
Measuring_rod
Solid with four equal triangular faces
A regular tetrahedron is a polyhedron with four equilateral triangular faces. A regular tetrahedron is a tetrahedron (that is, a four-sided polyhedron)
Regular_tetrahedron
Lebesgue-Stieltjes integration
Lebesgue–Stieltjes measure, which may be associated to any function of bounded variation on the real line. The Lebesgue–Stieltjes measure is a regular Borel measure, and
Lebesgue–Stieltjes integration
Lebesgue–Stieltjes_integration
Broadest definition of sizes in integer-dimensional spaces
(A\setminus F)=0} . Lebesgue measure is both locally finite and inner regular, and so it is a Radon measure. Lebesgue measure is strictly positive on non-empty
Lebesgue_measure
Function from sets to numbers
\}.} regular if it is both inner regular and outer regular. a Borel regular measure if it is a Borel measure that is also regular. a Radon measure if it
Set_function
Locally compact topological group with an invariant averaging operation
nontrivial ring measure, the Haar measure. (This is a Borel regular measure when G is second-countable; the left and right Haar measures coincide when G
Amenable_group
Measure which assigns zero to every measurable set
condition to be a regular measure. μ is never a strictly positive measure, regardless of (X, Σ), since every measurable set has zero measure. Since μ(X) = 0
Trivial_measure
Four-dimensional analogues of the regular polyhedra in three dimensions
their 3-dimensional analogues, the convex regular 4-polytopes can be naturally ordered by size as a measure of 4-dimensional content (hypervolume) for
Regular_4-polytope
Concept in probability theory
we can decompose μ {\displaystyle \mu } into a sum of a regular measure and an atomic measure: μ = μ r + μ s {\displaystyle \mu =\mu _{r}+\mu _{s}} .
Maxwell's_theorem
Roman Catholic priests living in community under a religious rule
The Canons Regular are Catholic priests and religious brothers (canons) who live in community under a rule (Latin: regula and κανών, kanon, in Greek)
Canon_regular
distribution of consumers' endowments, is regular. In technical terms, the set of nonregular economies is of Lebesgue measure zero. Combined with the index theorem
Regular_economy
Type of Borel measure
In mathematics, a Gaussian measure is a Borel measure on finite-dimensional Euclidean space R n {\displaystyle \mathbb {R} ^{n}} , closely related to the
Gaussian_measure
specifically, in geometric measure theory — spherical measure σn is the "natural" Borel measure on the n-sphere Sn. Spherical measure is often normalized so
Spherical_measure
Oregon drug reclassification bill
In November 2020, voters in the U.S. state of Oregon passed Ballot Measure 110, "[reclassifying] possession/penalties for specified drugs". It reclassifies
2020 Oregon Ballot Measure 110
2020_Oregon_Ballot_Measure_110
Mathematical concept
tightness used in the analysis of regular measures in metric spaces For σ {\displaystyle \sigma } -finite measure spaces, it can be shown that if a family
Uniform_integrability
Lebesgue measure Lebesgue integration Lebesgue's density theorem Counting measure Complete measure Haar measure Outer measure Borel regular measure Radon
List of integration and measure theory topics
List_of_integration_and_measure_theory_topics
Polytope with highest degree of symmetry
the measure polytopes or hypercubes. Their names are, in order of dimension: 0. Point 1. Line segment 2. Square (regular tetragon) 3. Cube (regular hexahedron)
Regular_polytope
the case that μ is a Radon measure, and hence inner regular, the measure μ and its inner measure coincide, so the μ-measure of G is then 0 or 1.) Borell
Convex_measure
Proof that every structure with certain properties is isomorphic to another structure
versions, one of them identifying the dual space of C0(X) with the set of regular measures on X. The Whitney embedding theorems embed any abstract manifold in
Representation_theorem
Distributions on spaces of differential forms
current such that M(T) < ∞ is representable by integration of a regular Borel measure by a version of the Riesz representation theorem. This is the starting
Current_(mathematics)
Concept in mathematics
mathematics, the support (sometimes topological support or spectrum) of a measure μ {\displaystyle \mu } on a measurable topological space ( X , Borel
Support_(measure_theory)
American and Canadian Baptist group
doctrine" and "affirm the rule or measure of the Scripture." As compared to General Baptists or Free Baptists, Regular Baptists were strict in their beliefs
Regular_Baptists
Specifications for quantities of ingredients
volume worldwide, as few households have sufficiently precise balances to measure by weight. In most countries, meat is described by weight or count: "a
Cooking_weights_and_measures
Theory of generalized measures in mathematics
called a fuzzy measure. A fuzzy measure is called normalized or regular if g ( X ) = 1 {\displaystyle g(\mathbf {X} )=1} . A fuzzy measure is: additive
Fuzzy_measure_theory
Drinking and serving glass for beer
definition of a pint differs by country, thus a pint glass will reflect the regular measure of beer in that country. In the UK, law stipulates that a serving of
Beer_glassware
Measure on group representations
describes how the regular representation breaks up into irreducible unitary representations. In some cases the term Plancherel measure is applied specifically
Plancherel_measure
Words that measure quantities
In linguistics, measure words are words (or morphemes) that are used in combination with a numeral to indicate an amount of something represented by some
Measure_word
Consistent set of finite-dimensional distributions will define a stochastic process
suppose we have a probability measure μ F {\displaystyle \mu _{F}} on Ω F {\displaystyle \Omega _{F}} which is inner regular with respect to the product
Kolmogorov_extension_theorem
of England measures, which are the legislation of the Church of England. Some of these measures may have been repealed. Since 1970, measures have been
List of Church of England measures
List_of_Church_of_England_measures
The following is a list of ballot measures, whether initiated by legislators or citizens, which were certified to appear on various states' ballots during
2026 United States ballot measures
2026_United_States_ballot_measures
Oregon Ballot Measure 114, the Reduction of Gun Violence Act, is an Oregon state initiative that was narrowly approved by voters on November 8, 2022.
2022 Oregon Ballot Measure 114
2022_Oregon_Ballot_Measure_114
Kenyan track and field athlete (1952–2024)
regional meet on a course that was said to be 80 m (87 yd) short of the regular measure). He was also NCAA steeplechase champion in 1978 and 1979 and NCAA
Henry_Rono
locally compact Hausdorff space X . {\displaystyle X.} Consider a Borel regular measure μ {\displaystyle \mu } on X , {\displaystyle X,} and a functional ψ
Positive_linear_functional
British actress (born 1961)
has appeared in the 2000 miniseries Frank Herbert's Dune and as a series regular in Luther (2010), Shetland (2016) and Slow Horses (2022–present). Saskia
Saskia_Reeves
Russian mathematician (born 1956)
and its relations to geometric measure theory". In 2024, the article "On the uniform rectifiability of AD-regular measures with bounded Riesz transform
Alexander_Volberg
understanding of customers’ needs. We measure customer satisfaction systematically and frequently. We have routine or regular measures of customer service. We are
Market_orientation
Polygonal chain whose vertices are not all coplanar
have at least four vertices. The interior surface and corresponding area measure of such a polygon is not uniquely defined. Skew infinite polygons (apeirogons)
Skew_polygon
American mathematician
as well as computer science. Borel measure Borel regular measure Swift, George (1955), "Irregular Borel measures on topological spaces", Duke Mathematical
George_Herbert_Swift_Jr
Appalachian religious denomination
in Old Regular Baptist records or usage uses the "Measure of Faith" to mean a gift to the regenerated and not the unregenerated. Old Regular Baptists
Old_Regular_Baptists
Average income of an economy
conducted regular surveys among its 38 member countries using a standardized methodology and set of questions. Per capita income is often used to measure a sector's
Per_capita_income
British actress (born 1965)
(2005) The Light of Knowledge by Mya Hnuang Nyo, BBC Radio 4, (2005) Measure for Measure by William Shakespeare, BBC Radio 4, (2005) Bed and Breakfast by
Claire_Skinner
Shape with four equal sides and angles
In geometry, a square is a regular quadrilateral. It has four straight sides of equal length and four equal angles. Squares are special cases of rectangles
Square
significantly more than regular legislators. The Massachusetts Senate challenged the proposed measure, along with another measure concerning an expansion
2026 Massachusetts ballot measures
2026_Massachusetts_ballot_measures
is the essential infimum. A conditional risk measure ρ t {\displaystyle \rho _{t}} is said to be regular if for any X ∈ L T ∞ {\displaystyle X\in L_{T}^{\infty
Dynamic_risk_measure
topology. In practice, the use of Baire measures on Baire sets can often be replaced by the use of regular Borel measures on Borel sets. Baire sets were introduced
Baire_set
British actress (born 1966)
Pride and Prejudice fans". Wales Online. Retrieved 5 June 2026. "Measure For Measure (1994)". British Film Institute. Retrieved 5 June 2026. Frederick
Juliet_Aubrey
Figure formed by two rays meeting at a common point
magnitude as associated quantity. Angular measure or measure of angle are sometimes used to distinguish between the measure of the quantity and figure itself
Angle
British actress (born 1981)
for the Prosecution (2016). Her stage credits include Miss Julie, Measure for Measure (both 2006), and Anton Chekhov's Ivanov (2008). Riseborough was born
Andrea_Riseborough
Polytope constructed from alternation of a hypercube
(Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3–45] Olshevsky, George. "Half measure polytope". Glossary for
Demihypercube
1985 single by Icehouse
single issued from the band's 1986 album, Measure for Measure. The single was released in Australia through Regular Records, on 7", 12" and maxi-cassette
No_Promises_(Icehouse_song)
Under Measure 113, the state Constitution was amended so that state Senators and state Representatives with ten unexcused absences from either a regular or
2022 Oregon Ballot Measure 113
2022_Oregon_Ballot_Measure_113
Ballot measure in Los Angeles County, California for transportation projects
Measure R was a ballot measure during the November 2008 elections in Los Angeles County, California, that proposed a half-cent sales taxes increase on
2008 Los Angeles County Measure R
2008_Los_Angeles_County_Measure_R
fundamental approaches to constructing measures of network similarity: structural equivalence, automorphic equivalence, and regular equivalence. There is a hierarchy
Similarity_(network_science)
The following is a list of ballot measures, whether initiated by legislators or citizens, which were certified to appear on various states' ballots during
2024 United States ballot measures
2024_United_States_ballot_measures
\langle E(B)x,y\rangle } is a regular Borel measure, meaning all compact sets have finite total variation and the measure of a set can be approximated
Naimark's_dilation_theorem
Hungarian and American mathematician and physicist (1903–1957)
showing that the ergodic measure preserving actions of the real line are the fundamental building blocks from which all measure-preserving actions can be
John_von_Neumann
Scottish actor (born 1962)
several years before during a studio production of Shakespeare's Measure for Measure. In many of his interviews, he mentions stories from their relationship
John_Hannah_(actor)
Theorem in measure theory
a result in measure theory and probability theory. It rigorously defines the idea of a non-trivial "restriction" of a measure to a measure zero subset
Disintegration_theorem
Off-beat rhythm
is played on the second beat of a 3 4 measure or a dominant chord is played at the fourth beat of a 4 4 measure. The latter occurs frequently in tonal
Syncopation
equivalent (APE) is a measure used for comparison of life insurance revenue by normalising policy premiums into the equivalent of regular annual payments.
Annual_premium_equivalent
English actor
November 2001. Billington, Michael (8 November 2002). "Theatre - Measure for Measure Malaya". The Guardian. Retrieved 11 February 2022. Jones, Sarah (22
Richard_Dillane
United States military engineering metric
Technical performance measures (TPM) is a term used by the US military to refer to key technical goals that needed to be met, where the technical goals
Technical_performance_measure
Polygon with 13 edges
thirteen-sided polygon. A regular tridecagon is represented by Schläfli symbol {13}. The measure of each internal angle of a regular tridecagon is approximately
Tridecagon
Imperial unit and U.S. customary unit of area
the pluralization is regular in the noun form, when used as an adjective, the singular is preferred. So, an apartment measuring 700 square feet could
Square_foot
Device that produces a sound at a regular interval
A metronome (from Ancient Greek μέτρον (métron) 'measure' and νόμος (nómos) 'law') is a device that produces an audible click or other sound at a uniform
Metronome
Australian actor
appearances in the Mad Max film franchise as The People Eater, as well as his regular roles in television series and soap operas All Saints, Blue Heelers, SeaChange
John Howard (Australian actor)
John_Howard_(Australian_actor)
System of measurements
in the British Weights and Measures Act 1824 and which continued to be developed through a series of Weights and Measures Acts and amendments. The imperial
Imperial_units
Similarity measure for number sequences
In data analysis, cosine similarity is a measure of similarity between two non-zero vectors defined in an inner product space. Cosine similarity is the
Cosine_similarity
Tiling of the plane by pentagons
regular pentagon, 108°, is not a divisor of 360°, the angle measure of a whole turn. However, regular pentagons can tile the hyperbolic plane with four pentagons
Pentagonal_tiling
Branch of mathematics
and volume are extended by measure theory, which studies methods of assigning a size or measure to sets, where the measures follow rules similar to those
Geometry
Type of metric change in music
comparison to common-time. Thus, two measures of 4 4 approximate a single measure of 8 8, while a single measure of 4/4 emulates 2/2. Half-time is not
Half-time_(music)
Type of group representation for locally compact groups
subrepresentation of the left regular representation of G on L²(G). In the Plancherel measure, such representations have positive measure. The name comes from
Discrete series representation
Discrete_series_representation
Counterintuitive observation
Mandelbrot. The measured length of the coastline depends on the method used to measure it and the degree of cartographic generalization. Since a landmass has
Coastline_paradox
Church of England measure
church. In 2003, the measure was amended by the Synodical Government (Amendment) Measure 2003 (No. 1) so that there would be a regular review of the arrangements
Synodical Government Measure 1969
Synodical_Government_Measure_1969
Geometrical measure
In plane geometry the Estermann measure is a number defined for any bounded convex set describing how close to being centrally symmetric it is. It is
Estermann_measure
English actor and playwright (born 1955)
Archived from the original on 26 July 2012. Retrieved 24 October 2012. "Measure for Measure". Rscshakespeare.co.uk. Archived from the original on 28 April 2012
David_Haig
travel, tourism, insurance
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