Borel measurable function

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• 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

• Weakly measurable function — See also= In mathematics mdash; specifically, in functional analysis mdash; a weakly measurable function taking values in a Banach space is a function whose composition with any element of the dual space is a measurable function in the usual… …   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 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 function — noun A function which is Borel measurable …   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 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

• Probability density function — Boxplot and probability density function of a normal distribution N(0, σ2). In probability theory, a probability density function (pdf), or density of a continuous random variable is a function that describes the relative likelihood for this… …   Wikipedia

• Itō diffusion — In mathematics mdash; specifically, in stochastic analysis mdash; an Itō diffusion is a solution to a specific type of stochastic differential equation. Itō diffusions are named after the Japanese mathematician Kiyoshi Itō.OverviewA (time… …   Wikipedia