An Introduction to the Theory of Real Functions
Stanislaw Lojasiewicz
Wiley
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.