Study An Introduction to the Theory of Real Functions (0471914142)

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Stanislaw Lojasiewicz "An Introduction to the Theory of Real Functions"

This detailed and thorough introduction to classical real analysis covers both elementary and advanced material. The book also includes a number of topics not normally found in books at this level. Examples are Helly's theorems on sequences of monotone functions; Tonelli polynomials; Bernstein polynomials and absolutely monotone functions; and the theorems of Rademacher and Stepanov on differentiability of Lipschitz continuous functions. A knowledge of the elements of set theory, topology, and differential and integral calculus is required and the book also includes a large number of exercises.

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