countably additive
Look at other dictionaries:
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. * * * … Universalium
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
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
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
Direct integral — In mathematics and functional analysis a direct integral is a generalization of the concept of direct sum. The theory is most developed for direct integrals of Hilbert spaces and direct integrals of von Neumann algebras. The concept was… … Wikipedia
Measurable cardinal — In mathematics, a measurable cardinal is a certain kind of large cardinal number. Contents 1 Measurable 2 Real valued measurable 3 See also 4 References … 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
