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...y measures assign a value lesser than or equal to 1 to the underlying set. In measure theory, the following implications hold between measures: ...

In [[mathematics]], in the field of [[measure theory]], '''τ-additivity''' is a certain property of [[Measure (mathematics)|meas ...is in <math>\Sigma,</math> the measure of the union is the [[supremum]] of measures of elements of <math>\mathcal{G};</math> that is,: ...

In the mathematical discipline of [[measure theory]], the '''intensity''' of a [[Measure (mathematics)|measure]] is the averag ...ich the intensity is well defined is a measurable subset of the set of all measures on <math> \R </math>. The mapping ...

{{Short description|Equivalence relation on mathematical measures}} ...ity measure]]s are "the same" from the point of view of [[large deviations theory]]. ...

...extension theorem''' is a result from [[measure theory]] and [[probability theory]] on extensions of [[probability measure]]s. The theorem makes a statement ...|first2=Jürgen |last2=Lehn |title=Two principles for extending probability measures |journal=Manuscripta Math. |number=21 |pages=43–50 |date=1977|volume=21 |do ...

...th respect to ''&mu;'' is "as big as it can be". The theory of maximising measures is relatively young and quite little is known about their general structure ...Let Inv(''T'') denote the set of all [[Borel measure|Borel]] probability measures on ''X'' that are [[invariant measure|invariant]] under ''T'', i.e., for ev ...

...tician]] [[Christer Borell]] was a pioneer of the detailed study of convex measures on [[locally convex space]]s in the 1970s.<ref name="Borell1974">{{cite jou | title = Convex measures on locally convex spaces ...

{{Short description|Theory in probability theory}} ...math> on a [[locally convex space]] <math>X</math> are either [[equivalent measures]] or else [[singular measure|mutually singular]]:<ref name="Bogachev">{{cit ...

...'mixed binomial process''' is a special [[point process]] in [[probability theory]]. They naturally arise from restrictions of ([[mixed Poisson process|mixed ...me that <math> K, X_1, X_2, \dots </math> are [[Independence (probability theory)|independent]] and let <math> \delta_x </math> denote the [[Dirac measure]] ...

...h>-dimensional [[Euclidean space]], for which it can be intuitive to study measures that are unchanged by rotations and translations. An obvious example of suc ...e and survival probability for unimodal Lévy processes|journal=Probability Theory and Related Fields|language=en|volume=162|issue=1–2|pages=155–198|doi=10.10 ...

...033-295x.84.4.327}}</ref> is an asymmetric [[similarity measure]] on [[set theory|sets]] that compares a variant to a prototype. The Tversky index can be see Here, <math>X \setminus Y</math> denotes the [[Complement (set theory)#Relative_complement|relative complement]] of Y in X. ...

...are a useful pedagogical tool for teaching and learning about these basic measures of information. Information diagrams have also been applied to specific pro ...)}}. The circle on the left (red and violet) is the [[Entropy (information theory)|individual entropy]] {{tmath|H(X)}}, with the red being the [[conditional ...

In [[measure theory]], the '''Euler measure''' of a [[polyhedral set]] equals the [[Euler integral]] of its [[indicator function]]. ...while the Euler measure of a ''d''-D [[Subspace topology|relative]]-[[Open set|open]] [[bounded convex polyhedron]] is <math>(-1)^d</math>.<ref name="Eule ...

...ty set''' of a [[measure (mathematics)|measure]] {{mvar|μ}} is any [[Borel set]] {{mvar|B}} such that ...[[random variable]] {{mvar|X}}, a set {{mvar|B}} is called a '''continuity set''' of {{mvar|X}} if ...

...he [[Jaccard index]] and is defined as the size of the [[intersection (set theory)|intersection]] divided by the size of the smaller of two sets: Note that <math>0 \leq \operatorname{overlap}(A,B) \leq 1</math>. If set ''A'' is a [[subset]] of ''B'' or the converse, then the overlap coefficien ...

...eory]], the '''Mitchell order''' is a [[well-founded]] [[preorder]] on the set of [[normal measure]]s on a [[measurable cardinal]] ''κ''. It is named for ...ed on the set (or [[proper class]], as the case may be) of [[extender (set theory)|extender]]s for ''κ''; but if it is so defined it may fail to be [[transit ...

...Technology]]</ref> is a type of integral with respect to a [[fuzzy measure theory|fuzzy measure]]. The Sugeno integral over the crisp set <math>A \subseteq X</math> of the function <math>h</math> with respect to t ...

In the theory of [[stochastic process]]es, a '''ν-transform''' is an operation that trans === For measures === ...

In [[mathematics]] &mdash; specifically, in [[geometric measure theory]] &mdash; '''spherical measure''' ''&sigma;''^''n'' is the "natur ...idate ''&sigma;''^''n'''s have been normalized to be probability measures, they are all the same measure. ...

...ometric measure theory]] an '''approximate tangent space''' is a [[measure theory|measure theoretic]] generalization of the concept of a [[tangent space]] fo ...space. This turns out to be the correct point of view in geometric measure theory. ...