Measure Theory (Graduate Texts in Mathematics 18)
by Paul R. Halmos · Springer
Classic graduate text whose opening chapters develop rings, sigma-rings, sigma-algebras, generated classes, the monotone class lemma, outer measures and the extension theorem at a level of detail modern books compress, before measurable functions and integration are reached. Chapters I-III (Sets and Classes, Measures and Outer Measures, Extension of Measures) are the fullest classical treatment of exactly what this topic covers.
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