この商品を友人に教える:
Strange Functions in Real Analysis Alexander Kharazishvili 第2 版
Strange Functions in Real Analysis
Alexander Kharazishvili
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.
432 pages
| メディア | 書籍 Paperback Book (ソフトカバーで背表紙を接着した本) |
| リリース済み | 2019年9月5日 |
| ISBN13 | 9780367391461 |
| 出版社 | Taylor & Francis Ltd |
| ページ数 | 432 |
| 寸法 | 150 × 220 × 10 mm · 566 g |
| 言語 | 英語 |
