product measure

Let (E1,1(E1)) and (E2,2(E2)) be two measurable spacesMathworldPlanetmathPlanetmath, with measuresMathworldPlanetmath μ1 and μ2. Let 1×2 be the sigma algebra on E1×E2 generated by subsets of the form B1×B2, where B11(E1) and B22(E2).

The product measureMathworldPlanetmath μ1×μ2 is defined to be the unique measure on the measurable space (E1×E2,1×2) satisfying the property

μ1×μ2(B1×B2)=μ1(B1)μ2(B2) for all B11(E1),B22(E2).
Title product measure
Canonical name ProductMeasure
Date of creation 2013-03-22 12:00:33
Last modified on 2013-03-22 12:00:33
Owner djao (24)
Last modified by djao (24)
Numerical id 7
Author djao (24)
Entry type Definition
Classification msc 28A35