This book deals with topics usually studied in a masters or
graduate level course on the theory of measure and integration. It
starts with the Riemann integral and points out some of its
shortcomings which motivate the theory of measure and the Lebesgue
integral. Starting with abstract measures and outermeasures, the
Lebesgue measure is constructed and its important properties are
highlighted. Measurable functions, different notions of
convergence, the Lebesgue integral, the fundamental theorem of
calculus, product spaces, and signed measures are studied. There is
a separate chapter on the change of variable formula and one on Lp-
spaces. Most of the material in this book can be covered in a one
semester course. The prerequisite for following this book is
familiarity with basic real analysis and elementary topological
notions, with special emphasis on the topology of the N-
dimensional euclidean space. Each chapter is provided with a
variety of exercises.
General
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