Borel function
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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 equivalence relation — In mathematics, a Borel equivalence relation on a Polish space X is an equivalence relation on X that is a Borel subset of X times; X (in the product topology).Given Borel equivalence relations E and F on Polish spaces X and Y respectively, one… … Wikipedia
Borel measurable — adjective 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 … Wiktionary
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 summation — In mathematics, a Borel summation is a generalisation of the usual notion of summation of a series. In particular it gives a definition of a quantity that in many ways behaves formally like the sum, even if the series is in fact… … 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 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-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–Carathéodory theorem — In mathematics, the Borel–Carathéodory theorem in complex analysis shows that an analytic function may be bounded by its real part. It is an application of the maximum modulus principle. It is named for Émile Borel and Constantin Carathéodory.… … Wikipedia
Function (mathematics) — f(x) redirects here. For the band, see f(x) (band). Graph of example function, In mathematics, a function associates one quantity, the a … Wikipedia
