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Problems in Analysis

Problems in Analysis
Catalogue Information
Field name Details
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 0941-3502
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, 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 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/10.1007/978-1-4615-7679-2
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