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Universalium. 2010.
countably additive function — Math. a set function that upon operating on the union of a countable number of disjoint sets gives the same result as the sum of the functional values of each set. Cf. finitely additive function … Useful english dictionary
finitely additive function — Math. a set function that upon operating on the union of a finite number of disjoint sets gives the same result as the sum of the functional values of each set. Cf. countably additive function. * * * … Universalium
finitely additive function — Math. a set function that upon operating on the union of a finite number of disjoint sets gives the same result as the sum of the functional values of each set. Cf. countably additive function … Useful english dictionary
Convex function — on an interval. A function (in black) is convex if and only i … Wikipedia
Vector measure — In mathematics, a vector measure is a function defined on a family of sets and taking vector values satisfying certain properties. Definitions and first consequencesGiven a field of sets (Omega, mathcal F) and a Banach space X, a finitely… … Wikipedia
Projection-valued measure — In mathematics, particularly functional analysis a projection valued measure is a function defined on certain subsets of a fixed set and whose values are self adjoint projections on a Hilbert space. Projection valued measures are used to express… … Wikipedia
Vitali–Hahn–Saks theorem — In mathematics, the Vitali–Hahn–Saks theorem states that given mu;n for each integer n >0, a countably additive function defined on a fixed sigma algebra Sigma;, with values in a given Banach space B , such that :lim {n ightarrow infty} mu n(X)… … 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
Riesz representation theorem — There are several well known theorems in functional analysis known as the Riesz representation theorem. They are named in honour of Frigyes Riesz. The Hilbert space representation theorem This theorem establishes an important connection between a … Wikipedia
Axiom of choice — This article is about the mathematical concept. For the band named after it, see Axiom of Choice (band). In mathematics, the axiom of choice, or AC, is an axiom of set theory stating that for every family of nonempty sets there exists a family of … Wikipedia
