Hahn-Kolmogorov theorem

Let 𝒜0 be an algebraMathworldPlanetmath of subsets of a set X. If a finitely additive measure μ0:𝒜{} satisfies


for any disjoint family {An:n} of elements of 𝒜0 such that n=0An𝒜0, then μ0 extends to a measure defined on the σ-algebra 𝒜 generated by 𝒜0; i.e. there exists a measure μ:𝒜{} such that its restrictionPlanetmathPlanetmathPlanetmath (http://planetmath.org/RestrictionOfAFunction) to 𝒜0 coincides with μ0.

If μ0 is σ-finite (http://planetmath.org/SigmaFinite), then the extensionPlanetmathPlanetmath is unique.

Title Hahn-Kolmogorov theorem
Canonical name HahnKolmogorovTheorem
Date of creation 2013-03-22 14:03:10
Last modified on 2013-03-22 14:03:10
Owner Koro (127)
Last modified by Koro (127)
Numerical id 7
Author Koro (127)
Entry type Theorem
Classification msc 28A10
Synonym Hahn-Kolmogorov extension theorem
Synonym Kolmogorov extension theorem