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.
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© 1996 Springer-Verlag New York, Inc.
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Simonnet, M. (1996). Images of Radon Measures and Product Measures. In: Measures and Probabilities. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4012-9_21
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DOI: https://doi.org/10.1007/978-1-4612-4012-9_21
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