- Borel measurable
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Said of a function: that the inverse image of any open set in its codomain is a Borel set of its domain.See Also: Borel function
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Borel measurable
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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 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
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 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 function — noun A function which is Borel measurable … Wiktionary
Measurable function — In mathematics, particularly in measure theory, measurable functions are structure preserving functions between measurable spaces; as such, they form a natural context for the theory of integration. Specifically, a function between measurable… … Wikipedia
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 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
Borel determinacy theorem — In descriptive set theory, the Borel determinacy theorem shows that any Gale Stewart game whose winning set is a Borel set is determined, meaning that one of the two players will have a winning strategy for the game. It was proved by Donald A.… … 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
