The three volumes of A Course in Mathematical Analysis provide a
full and detailed account of all those elements of real and complex
analysis that an undergraduate mathematics student can expect to
encounter in the first two or three years of study. Containing
hundreds of exercises, examples and applications, these books will
become an invaluable resource for both students and instructors.
Volume 1 focuses on the analysis of real-valued functions of a real
variable. Volume 2 goes on to consider metric and topological
spaces. This third volume develops the classical theory of
functions of a complex variable. It carefully establishes the
properties of the complex plane, including a proof of the Jordan
curve theorem. Lebesgue measure is introduced, and is used as a
model for other measure spaces, where the theory of integration is
developed. The Radon-Nikodym theorem is proved, and the
differentiation of measures discussed.
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