Operations on Regular Measures
22.1 We have seen in Chapter 8 that we can associate a regular measure μ with a Radon measure λ, that is, a continuous linear functional on a space of continuous functions with compact support. We describe herein the functionals associated with the induced measures μ Y , the measures gμ that have a density with respect to μ, and the image measures π(μ).
22.2 We define the σ-ring of Baire sets in a locally compact space.
22.3 We use the results of Section 22.2 to show that the product, μ, of two regular measures, μ′ and μ″, is also a regular measure, provided that the compact sets of the product space are μ-immeasurable (Theorem 22.3.1).
22.4 Section 22.1 allows us to complete the results obtained in Chapter 11 on the change of variable formula.
KeywordsCompact Subset Radon Measure Variable Formula Countable Union Compact Hausdorff Space
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