Strange Functions in Real Analysis - Couverture rigide

Kharazishvili, Alexander

Couverture rigide

ISBN 10 : 1584885823 ISBN 13 : 9781584885825

Editeur : Chapman & Hall/CRC, 2005

Synopsis

Strange Functions in Real Analysis Explores a number of important examples and constructions of pathological functions. This work begins with Cantor and Peano-type functions and moves to functions whose constructions require essentially noneffective methods. It considers examples of functions whose existence cannot be established without the help of addition set-theoretical axioms. Full description

A propos du livre

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.

Détails de l'édition

• Éditeur: Chapman & Hall/CRC
• Date d'édition: 2005
• ISBN 10: 1584885823
• ISBN 13: 9781584885825
• Reliure: Relié
• Langue: anglais
• Numéro d'édition: 2
• Nombre de pages: 432