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Kharazishvili A. — Strange Functions in Real Analysis, Second Edition (Pure and Applied Mathematics)
Kharazishvili A. — Strange Functions in Real Analysis, Second Edition (Pure and Applied Mathematics)

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Название: Strange Functions in Real Analysis, Second Edition (Pure and Applied Mathematics)

Автор: Kharazishvili A.

Аннотация:

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.


Язык: en

Рубрика: Разное/

Статус предметного указателя: Неизвестно

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Издание: 2nd

Год издания: 2006

Количество страниц: 420

Добавлена в каталог: 18.02.2018

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