# Problems in Analysis

• Bernard R. Gelbaum
Book

Part of the Problem Books in Mathematics book series (PBM)

1. Front Matter
Pages i-vii
2. ### Problems

1. Front Matter
Pages 1-1
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Pages 3-4
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Pages 5-7
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Pages 8-9
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Pages 10-14
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Pages 15-19
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Pages 20-22
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Pages 23-27
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Pages 28-30
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Pages 35-37
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3. ### Solutions

1. Front Matter
Pages 65-65
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Pages 67-68
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Pages 69-75

### Introduction

These problems and solutions are offered to students of mathematics who have learned real analysis, measure theory, elementary topology and some theory of topological vector spaces. The current widely used texts in these subjects provide the background for the understanding of the problems and the finding of their solutions. In the bibliography the reader will find listed a number of books from which the necessary working vocabulary and techniques can be acquired. Thus it is assumed that terms such as topological space, u-ring, metric, measurable, homeomorphism, etc., and groups of symbols such as AnB, x EX, f: IR 3 X 1-+ X 2 - 1, etc., are familiar to the reader. They are used without introductory definition or explanation. Nevertheless, the index provides definitions of some terms and symbols that might prove puzzling. Most terms and symbols peculiar to the book are explained in the various introductory paragraphs titled Conventions. Occasionally definitions and symbols are introduced and explained within statements of problems or solutions. Although some solutions are complete, others are designed to be sketchy and thereby to give their readers an opportunity to exercise their skill and imagination. Numbers written in boldface inside square brackets refer to the bib­ liography. I should like to thank Professor P. R. Halmos for the opportunity to discuss with him a variety of technical, stylistic, and mathematical questions that arose in the writing of this book. Buffalo, NY B.R.G.

### Keywords

Analysis /Aufgabensammlung calculus measure measure theory real analysis

#### Authors and affiliations

• Bernard R. Gelbaum
• 1
1. 1.Department of MathematicsState University of New YorkBuffaloUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4615-7679-2
• Copyright Information Springer-Verlag New York 1982
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4615-7681-5
• Online ISBN 978-1-4615-7679-2
• Series Print ISSN 0941-3502