Images of Radon Measures and Product Measures

Summary

21.1 Let T, X be two locally compact spaces, μ a positive Radon measure on T, and π a µ-measurable mapping from T into X such that g o π is essentially μ-integrable for every g ∈ ℋ(X, C). Denote by ν the image measure, f ↦ ∫(f o π) dμ, of μ under π. Then ∫^• f dv = ∫^•(f o π) dμ for every function f ∶ X → [0,+∞]. A mapping f from X into a topological space is ν-measurable when f o π is μ-measurable (Theorem 21.1.1).

21.2 We study the decomposition of a measure in slices. This decomposition will be used in Chapter 23.

21.3 We define the product of two Radon measures.