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- ...ure]], and as such, it finds applications in measure theory, [[probability theory]], and [[theoretical computer science]]. ==Domain/Measure theory definition== ...7 KB (1,016 words) - 20:55, 28 June 2022
- ...rable space]]s is defined to be the finest such that the [[Projection (set theory)|projection mappings]] will be [[measurable function|measurable]]. Sometime ...is N. Moschovakis | author=Moschovakis, Yiannis N. | title=Descriptive Set Theory|url=https://www.math.ucla.edu/~ynm/books.htm | publisher=North Holland | ye ...6 KB (848 words) - 22:39, 5 April 2023
- ...tensity''' of a [[Measure (mathematics)|measure]] is the average value the measure assigns to an interval of length one. Let <math> \mu </math> be a measure on the real numbers. Then the intensity <math> \overline \mu </math> of <ma ...2 KB (242 words) - 17:39, 11 November 2022
- In mathematics, in particular in [[measure theory]], there are different notions of '''distribution function''' and it is im ...distribution function|distribution functions (in the sense of probability theory)]]. ...6 KB (939 words) - 21:23, 31 March 2024
- {{Short description|Area formula from geometric measure theory}} ...[geometric measure theory]] the '''area formula''' relates the [[Hausdorff measure]] of the image of a [[Lipschitz map]], while accounting for multiplicity, t ...3 KB (480 words) - 10:28, 9 November 2023
- ...can be used, for example, to determine whether a translate of a [[Gaussian measure]] <math>\mu</math> is equivalent to <math>\mu</math> (only when the transla [[Category:Theorems in measure theory]] ...3 KB (393 words) - 22:36, 12 May 2024
Page text matches
- In [[measure theory]], the '''Euler measure''' of a [[polyhedral set]] equals the [[Euler integral]] of its [[indicator ==The magnitude of an Euler measure== ...990 bytes (129 words) - 17:19, 21 June 2023
- ...ory]], '''τ-additivity''' is a certain property of [[Measure (mathematics)|measure]]s on [[topological space]]s. ...such that its [[Union (set theory)|union]] is in <math>\Sigma,</math> the measure of the union is the [[supremum]] of measures of elements of <math>\mathcal{ ...1 KB (161 words) - 21:04, 28 June 2022
- ...[[Measure (mathematics)|measure]] that is closely related to [[probability measure]]s. While probability measures always assign the value 1 to the underl Let <math> \mu </math> be a [[Measure (mathematics)|measure]] on the [[measurable space]] <math> (X, \mathcal A) </math>. ...2 KB (238 words) - 06:46, 23 December 2021
- ...>. In [[incomplete market]]s, this is one way of choosing a [[risk-neutral measure]] (from the infinite number available) so as to still maintain the no-arbit ...e (probability theory)|martingale]]. For certain situations, the resultant measure <math>Q</math> will not be equivalent to <math>P</math>. ...2 KB (223 words) - 01:13, 14 December 2023
- ...ch of [[mathematics]], a '''continuity set''' of a [[measure (mathematics)|measure]] {{mvar|μ}} is any [[Borel set]] {{mvar|B}} such that ...topological) [[boundary (topology)|boundary]] of {{mvar|B}}. For [[signed measure]]s, one instead asks that ...1 KB (157 words) - 05:06, 13 February 2025
- {{Short description|Measure derived from a random measure}} ...d as a random measure, is for example uniquely determined by its intensity measure. <ref name="Klenke528" /> ...3 KB (407 words) - 15:48, 14 December 2024
- ...tensity''' of a [[Measure (mathematics)|measure]] is the average value the measure assigns to an interval of length one. Let <math> \mu </math> be a measure on the real numbers. Then the intensity <math> \overline \mu </math> of <ma ...2 KB (242 words) - 17:39, 11 November 2022
- ...em in the theory of [[point process]]es, a sub-discipline of [[probability theory]]. It describes how a [[Poisson point process]] is altered under [[measurab ...a [[Radon measure]] on <math> X </math> and assume that the [[pushforward measure]] ...1 KB (230 words) - 15:09, 12 November 2021
- In [[probability theory]], a '''mixed Poisson process''' is a special [[point process]] that is a g Let <math> \mu </math> be a [[locally finite measure]] on <math> S </math> and let <math> X </math> be a [[random variable]] wit ...1 KB (231 words) - 16:44, 12 May 2021
- {{Short description|Mathematical measure invariant under linear isometries}} ...a measure to [[subset]]s of ''n''-dimensional Euclidean space: [[Lebesgue measure]]. ...4 KB (627 words) - 22:06, 18 September 2024
- In [[potential theory]], a mathematical discipline, '''balayage''' (from French: ''[[wiktionary:f ...a [[Measure (mathematics)|measure]] ''μ'' on a closed domain ''D'' to a measure ''ν'' on the boundary ''∂ D'', so that the [[Newtonian potential]]s ...1 KB (210 words) - 18:39, 17 February 2024
- ...ntegral]] of ''f'' with respect to ''μ'' is "as big as it can be". The theory of maximising measures is relatively young and quite little is known about ...[[Borel measure|Borel]] probability measures on ''X'' that are [[invariant measure|invariant]] under ''T'', i.e., for every Borel-measurable subset ''A'' of ' ...3 KB (404 words) - 07:42, 27 April 2024
- ...e function on ''S'' then the Wiener–Wintner theorem states that there is a measure 0 set ''E'' such that the average ...ollows. The point of the Wiener–Wintner theorem is that one can choose the measure 0 exceptional set ''E'' to be independent of ''λ''. ...2 KB (234 words) - 10:04, 10 November 2024
- In [[mathematics]], a '''''G''-measure''' is a measure <math>\mu</math> that can be represented as the weak-∗ limit of a sequence ...>-1 < r < 1, m \in \mathbb N</math>. The weak-∗ limit of this product is a measure on the circle <math>\mathbb T</math>, in the sense that for <math> f \in C( ...2 KB (303 words) - 02:55, 13 July 2024
- ...e radius. Thus, if (''X'', ''d'') is a metric space, a Borel regular measure ''μ'' on ''X'' is said to be '''uniformly distributed''' if | title = On some measures analogous to Haar measure ...2 KB (288 words) - 06:32, 18 October 2022
- ...]]s. The theorem makes a statement about when one can extend a probability measure to a larger [[σ-algebra]]. It is of particular interest for infinite dimens == A measure extension theorem of Bierlein == ...3 KB (380 words) - 11:19, 18 June 2024
- ..., most famously the [[Haar measure]], and the study of [[stationary random measure]]s. ...r=2017 |title=Random Measures, Theory and Applications|series=Probability Theory and Stochastic Modelling |volume=77 |location= Switzerland |publisher=Sprin ...2 KB (325 words) - 13:12, 13 August 2023
- ...''ν-transform''' is an operation that transforms a [[measure (mathematics)|measure]] or a [[point process]] into a different point process. Intuitively the ν- ...on the point <math> x </math> and let <math> \mu </math> be a simple point measure on <math> S </math>. This means that ...3 KB (478 words) - 03:35, 3 November 2019
- {{Short description|Probability measure on a complex plane}} ...complex plane which may be viewed as an analog of the [[spectral counting measure]] (based on [[Eigenvalues and eigenvectors#Algebraic multiplicity|algebraic ...2 KB (322 words) - 14:40, 21 April 2024
- ...can be used, for example, to determine whether a translate of a [[Gaussian measure]] <math>\mu</math> is equivalent to <math>\mu</math> (only when the transla [[Category:Theorems in measure theory]] ...3 KB (393 words) - 22:36, 12 May 2024