Articles liés à Strange Functions in Real Analysis
Synopsis
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nonintegrable Lebesgue measurable functions. While dubbed strange or "pathological," these functions are ubiquitous throughout mathematics and play an important role in analysis, not only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis.
Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms and demonstrates that their existence follows from certain set-theoretical hypotheses, such as the Continuum Hypothesis.
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Présentation de l'éditeur
Weierstrass and Blancmange nowhere differentiable functions, Lebesgue integrable functions with everywhere divergent Fourier series, and various nonintegrable Lebesgue measurable functions. While dubbed strange or "pathological," these functions are ubiquitous throughout mathematics and play an important role in analysis, not only as counterexamples of seemingly true and natural statements, but also to stimulate and inspire the further development of real analysis.
Strange Functions in Real Analysis explores a number of important examples and constructions of pathological functions. After introducing the basic concepts, the author begins with Cantor and Peano-type functions, then moves to functions whose constructions require essentially noneffective methods. These include functions without the Baire property, functions associated with a Hamel basis of the real line, and Sierpinski-Zygmund functions that are discontinuous on each subset of the real line having the cardinality continuum. Finally, he considers examples of functions whose existence cannot be established without the help of additional set-theoretical axioms and demonstrates that their existence follows from certain set-theoretical hypotheses, such as the Continuum Hypothesis.
Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.
- ÉditeurChapman & Hall/CRC
- Date d'édition2005
- ISBN 10 1584885823
- ISBN 13 9781584885825
- ReliureRelié
- Langueanglais
- Numéro d'édition2
- Nombre de pages432
- Coordonnées du fabricantnon disponible
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Pure and Applied Mathematics: Strange Functions in Real Analysis
Edité par
Chapman & Hall, 2006
ISBN 10 : 1584885823
ISBN 13 : 9781584885825
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Etat : Good. This is an ex-library book and may have the usual library/used-book markings inside.This book has hardback covers. In good all round condition. No dust jacket. Please note the Image in this listing is a stock photo and may not match the covers of the actual item,900grams, ISBN:9781584885825. N° de réf. du vendeur 9898731
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Strange Functions in Real Analysis. Second Edition (Pure & Applied Mathematics. a Series of Monographs and Textbooks)
Edité par
Chapman and Hall/Crc, Boca Raton, Florida, 2006
ISBN 10 : 1584885823
ISBN 13 : 9781584885825
Ancien ou d'occasion
Couverture rigide
Vendeur : Literary Cat Books, Machynlleth, Powys, WALES, Royaume-Uni
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Original Boards. Etat : Near Fine. Etat de la jaquette : No Dust Jacket. Second Edition. Light wear to spine, covers & corners. ; Octavo; xii, 415 pages. N° de réf. du vendeur LCH47667
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Strange Functions in Real Analysis, Second Edition (Pure & Applied Mathematics)
Edité par
Chapman and Hall/CRC, 2005
ISBN 10 : 1584885823
ISBN 13 : 9781584885825
Ancien ou d'occasion
Couverture rigide
Vendeur : dsmbooks, Liverpool, Royaume-Uni
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hardcover. Etat : Very Good. Very Good. book. N° de réf. du vendeur D8S0-3-M-1584885823-3
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