Strange Functions in Real Analysis Second Edition is popular PDF and ePub book, written by Alexander Kharazishvili in 2005-12-20, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Strange Functions in Real Analysis Second Edition can be Read Online from any device for your convenience.
Strange Functions in Real Analysis Second Edition Book PDF Summary
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.
Detail Book of Strange Functions in Real Analysis Second Edition PDF
- Author : Alexander Kharazishvili
- Release : 20 December 2005
- Publisher : CRC Press
- ISBN : 9781420034844
- Genre : Mathematics
- Total Page : 428 pages
- Language : English
- PDF File Size : 13,9 Mb
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