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finitely additive measure

См. также в других словарях:

  • 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

  • Valuation (measure theory) — In measure theory or at least in the approach to it through domain theory, a valuation is a map from the class of open sets of a topological space to the set positive real numbers including infinity. It is a concept closely related to that of a… …   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

  • 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

  • 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

  • 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

  • Non-measurable set — This page gives a general overview of the concept of non measurable sets. For a precise definition of measure, see Measure (mathematics). For various constructions of non measurable sets, see Vitali set, Hausdorff paradox, and Banach–Tarski… …   Wikipedia

  • Banach–Tarski paradox — The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3 dimensional space can be split into several non overlapping pieces, which can then be put back together in a different way to yield two identical …   Wikipedia

  • Hausdorff paradox — In mathematics, the Hausdorff paradox, named after Felix Hausdorff, states that if you remove a certain countable subset of the sphere S ², the remainder can be divided into three subsets A , B and C such that A , B , C and B ∪ C are all… …   Wikipedia

  • Ultrafilter — In the mathematical field of set theory, an ultrafilter on a set X is a collection of subsets of X that is a filter, that cannot be enlarged (as a filter). An ultrafilter may be considered as a finitely additive measure. Then every subset of X is …   Wikipedia

  • Ba space — In mathematics, the ba space ba(Sigma) of an algebra of sets Sigma is the Banach space consisting of all bounded and finitely additive measures on Sigma. The norm is defined as the variation, that is | u|=| u|(X).… …   Wikipedia

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