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Textbook 2013Latest editionHausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on locally compact groups. This second edition includes a chapter on measure-theoretic probability theory, plus brief treatments of the Banach-Tarski paradox, the Henstock-Kurzweil integral, the Daniell integral, an
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1019-6242 the Daniell integral, and a brief introduction to measure-th.Intended as a self-contained introduction to measure theory, this textbook also includes a comprehensive treatment of integration on locally compact Hausdorff spaces, the analytic and Borel subsets of Polish spaces, and Haar measures on lo
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Product Measures,nite measures on two sets, we first define a natural product measure on the product of these sets (Section 5.1). Then we look at how integrals with respect to this product measure can be evaluated in terms of iterated integrals (Section 5.2). The chapter ends with a few applications (Section 5.3).
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Functions and Integrals,o its basic properties (Sections 2.3 and 2.4). The chapter ends with a sketch of how the Lebesgue integral relates to the Riemann integral (Section 2.5) and then with a few more details about measurable functions (Section 2.6).
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