Problems in Real Analysis


  • Charalambos Aliprantis, Purdue University, Indianapolis, U.S.A.
  • Owen Burkinshaw, Indiana University-Purdue University, Indianapolis , U.S.A.

A collection of problems and solutions in real analysis based on the major textbook, Principles of Real Analysis (also by Aliprantis and Burkinshaw), Problems in Real Analysis is the ideal companion for senior science and engineering undergraduates and first-year graduate courses in real analysis. It is intended for use as an independent source, and is an invaluable tool for students who wish to develop a deep understanding and proficiency in the use of integration methods. Problems in Real Analysis teaches the basic methods of proof and problem-solving by presenting the complete solutions to over 600 problems that appear in Principles of Real Analysis, Third Edition. The problems are distributed in forty sections, and cover the entire spectrum of difficulty.
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Graduate students and researchers in mathematics and science, including the social sciences.


Book information

  • Published: October 1998
  • ISBN: 978-0-12-050253-0


From Book News, Inc. First published in 1981 as a textbook for undergraduate seniors and first-year graduate students in math, this iteration adds Fourier analysis, a chapter on Hilbert spaces, and about 150 new problems of varying difficulty. Aliprantis (economics and mathematics, Purdue U.) and Burkinshaw (mathematical sciences, Indiana U., Purdue U.) focus on measure theory via the semiring approach and the Lebesgue integral as well as their applications. They also cover topology and continuity, normed spaces, and special topics in integration. A humanistic touch: brief biographies of historical contributors to real analysis are interwoven throughout the text. Book News, Inc.®, Portland, OR

Table of Contents

Fundamentals of Real AnalysisTopology and ContinuityThe Theory of MeasureThe Lebesgue IntegralNormed Spaces and Lp-SpacesHilbert SpacesSpecial Topics in Integration