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Название: Measure and Category: A Survey of the Analogies between Topological and Measure Spaces
Автор: Oxtoby J.
This is a book first published in the 70's and it has the advantage of being easy reading and short. It presents to the student with little background (a course of real analysis or calculus is all that is required, together with some familiarity with set theoretic reasoning) some of the classical and powerful results of measure and set theory and analysis in an elegant and modern way. It explores in a diversity of ways the analogies of measure and category and the uses of Baire and Borel's theorems. I believe it is one of the best introductions of measure theory that can be found in the literature.