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Using a contemporary approach and a lively style, Gelbaum combines real and complex analysis, covering all major topics. He discusses topology in three ways: via open sets, nets and filters. Features a detailed exploration of the link between measure as derived from a Daniell functional and classical Lebesgue-Caratheodory measure. Includes complete definitions of all mathematical concepts as well as numerous exercises and illustrations.

These counterexamples deal mostly with the part of analysis known as "real variables." The 1st half of the book discusses the real number system, functions and limits, differentiation, Riemann integration, sequences, infinite series, more. The 2nd half examines functions of 2 variables, plane sets, area, metric and topological spaces, and function spaces. 1962 edition. Includes 12 figures.

This text covers many principal topics in the theory of functions of a complex variable. These include, in real analysis, set algebra, measure and topology, real- and complex-valued functions, and topological vector spaces. In complex analysis, they include polynomials and power series, functions holomorphic in a region, entire functions, analytic continuation, singularities, harmonic functions, families of functions, and convexity theorems.