Strange Functions in Real Analysis, Second Edition - Rilegato

Kharazishvili, Alexander

Rilegato

ISBN 10: 1584885823 ISBN 13: 9781584885825

Casa editrice: Chapman and Hall/CRC, 2005

Riassunto

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.

Su questo libro

Contenuti

Introduction: basic concepts
Cantor and Peano type functions
Functions of first Baire class New!
Semicontinuous functions that are not countably continuous New!
Singular monotone functions
Everywhere differentiable nowhere monotone functions
Nowhere approximately differentiable functions
Blumberg's theorem and Sierpinski-Zygmund functions
Lebesgue nonmeasurable functions and functions without the Baire property
Hamel basis and Cauchy functional equation
Luzin sets, Sierpinski sets, and their applications
Absolutely nonmeasurable additive functions New!
Egorov type theorems
Sierpinski's partition of the Euclidean plane
Bad functions defined on second category sets New!
Sup-measurable and weakly sup-measurable functions
Generalized step-functions and superposition operators New!
Ordinary differential equations with bad right-hand sides
Nondifferentiable functions from the point of view of category and measure
Bibliography
Subject Index

Dettagli dell?edizione

• Editore: Chapman and Hall/CRC
• Data di pubblicazione: 2005
• ISBN 10: 1584885823
• ISBN 13: 9781584885825
• Rilegatura: Copertina rigida
• Lingua: Inglese
• Numero edizione: 2
• Numero di pagine: 432