Summary
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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© 1996 Springer-Verlag New York, Inc.
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Simonnet, M. (1996). Operations on Regular Measures. In: Measures and Probabilities. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-4012-9_22
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DOI: https://doi.org/10.1007/978-1-4612-4012-9_22
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-94644-3
Online ISBN: 978-1-4612-4012-9
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