Problems in Analysis

B. Gelbaum

ISBN 10: 1461576814 / ISBN 13: 9781461576815

Editore: Springer, Copernicus Dez 2012, 2012

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This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 240 pp. Englisch.

Codice articolo 9781461576815

Dati bibliografici

• Titolo: Problems in Analysis
• Editore: Springer, Copernicus Dez 2012
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461576814
• ISBN 13: 9781461576815
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 235 L x 155 A x 14 P (millimetri) 235 millimetri di larghezza per 155 millimetri di altezza per 14 millimetri di profondità
• Peso: 371 grammi

Descrizione articolo

Riassunto

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.

Contenuti

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.