countably additive measure

countably additive measure
счётно аддитивная мера

English-Russian scientific dictionary. 2008.

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  • countably additive — adjective Said of a measure: that it satisfies countable additivity …   Wiktionary

  • 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 algebra — In mathematics, a measure algebra is a Boolean algebra with a countably additive positive measure. A probability measure on a measure space gives a measure algebra on the Boolean algebra of measurable sets modulo null sets. Definition A measure… …   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

  • Haar measure — In mathematical analysis, the Haar measure is a way to assign an invariant volume to subsets of locally compact topological groups and subsequently define an integral for functions on those groups.This measure was introduced by Alfréd Haar, a… …   Wikipedia

  • Outer measure — In mathematics, in particular in measure theory, an outer measure or exterior measure is a function defined on all subsets of a given set with values in the extended real numbers satisfying some additional technical conditions. A general theory… …   Wikipedia

  • Signed measure — In mathematics, signed measure is a generalization of the concept of measure by allowing it to have negative values. Some authors may call it a charge,[1] by analogy with electric charge, which is a familiar distribution that takes on positive… …   Wikipedia

  • Cylinder set measure — In mathematics, cylinder set measure (or promeasure, or premeasure, or quasi measure, or CSM) is a kind of prototype for a measure on an infinite dimensional vector space. An example is the Gaussian cylinder set measure on Hilbert space. Cylinder …   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

  • Banach measure — In mathematics, Banach measure in measure theory may mean a real valued function on the algebra of all sets (for example, in the plane), by means of which a rigid, finitely additive area can be defined for every set, even when a set does not have …   Wikipedia

  • positive measure — noun A function whose domain is a σ algebra, whose codomain is [0,∞], and which is countably additive …   Wiktionary


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