Dewey Class 
515 
Title 
Problems in Analysis ([EBook] /) / by Bernard R. Gelbaum. 
Author 
Gelbaum, Bernard R. 
Other name(s) 
SpringerLink (Online service) 
Publication 
New York, NY : : Springer New York, , 1982. 
Physical Details 
VIII, 228 p. 1 illus. : online resource. 
Series 
Problem books in mathematics 09413502 
ISBN 
9781461576792 
Summary Note 
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, uring, 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 bibĀ 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.: 
Contents note 
Problems  1. Set algebra  2. Topology  3. Limits  4. Continuous functions  5. Functions from ?n to ?m  6. Measure and topology  7. General measure theory  8. Measures in ?n  9. Lebesgue measure in ?n  10. Lebesgue measurable functions  11. L1(X, ?)  12. L2(X, ?) or ? (Hilbert space)  13. Lp(X, ?), 1 ? p ? ?  14. Topological vector spaces  15. Miscellaneous problems  Solutions Pages  1. Set algebra  2. Topology  3. Limits  4. Continuous functions  5. Functions from ?n to ?m  6. Measure and topology  7. General measure theory  8. Measures in ?n  9. Lebesgue measure in ?n  10. Lebesgue measurable functions  11. L1(X, ?)  12. L2(X, ?) or ? (Hilbert space)  13. Lp(X, ?), 1 ? p ? ?  14. Topological vector spaces  15. Miscellaneous problems  Glossary of symbols  Index/Glossary. 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9781461576792 
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