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Borel measure
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Borel measure — In mathematics, the Borel algebra is the smallest sigma; algebra on the real numbers R containing the intervals, and the Borel measure is the measure on this sigma; algebra which gives to the interval [ a , b ] the measure b − a (where a < b… … Wikipedia
Borel — may refer to: * Émile Borel (1871–1956), a French mathematician * Armand Borel (1923–2003), a Swiss mathematician * Jacques Borel, a French novelist * Gabriel Borel, a French aircraft designer * Borel algebra, operating on Borel sets, named after … Wikipedia
Borel set — In mathematics, a Borel set is any set in a topological space that can be formed from open sets (or, equivalently, from closed sets) through the operations of countable union, countable intersection, and relative complement. Borel sets are named… … Wikipedia
Borel algebra — In mathematics, the Borel algebra (or Borel sigma; algebra) on a topological space X is a sigma; algebra of subsets of X associated with the topology of X . In the mathematics literature, there are at least two nonequivalent definitions of this… … Wikipedia
Borel regular measure — In mathematics, an outer measure mu; on n dimensional Euclidean space R n is called Borel regular if the following two conditions hold:* Every Borel set B sube; R n is mu; measurable in the sense of Carathéodory s criterion: for every A sube; R n … Wikipedia
Measure (mathematics) — Informally, a measure has the property of being monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B. Furthermore, the measure of the empty set is required to be 0. In mathematical analysis … Wikipedia
measure theory — noun A branch of mathematical analysis, concerned with the theory of integration, that generalizes the intuitive notions of length, area and volume. See Also: Borel measure, complex measure, Haar measur … Wiktionary
Borel functional calculus — In functional analysis, a branch of mathematics, the Borel functional calculus is a functional calculus (that is, an assignment of operators from commutative algebras to functions defined on their spectrum), which has particularly broad… … Wikipedia
Borel-Cantelli lemma — In probability theory, the Borel Cantelli lemma is a theorem about sequences of events. In a slightly more general form, it is also a result in measure theory. It is named after Émile Borel and Francesco Paolo Cantelli.Let ( E n ) be a sequence… … Wikipedia
Borel right process — Let E be a locally compact separable metric space.We will denote by mathcal E the Borel subsets of E.Let Omega be the space of right continuous maps from [0,infty) to E that have left limits in E,and for each t in [0,infty), denote by X t the… … Wikipedia
