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.
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