Strange functions in real analysis A.B. Kharazishvili. Pure and applied mathematics 272/2.

Kharazishvili, Alexander

ISBN 10: 1584885823 / ISBN 13: 9781584885825

Published by Boca, Chapman & Hall/CRC, 2006

About this Item

Ex-library with stamp and library-signature. GOOD condition, some traces of use. Ancien Exemplaire de bibliothèque avec signature et cachet. BON état, quelques traces d'usure. Ehem. Bibliotheksexemplar mit Signatur und Stempel. GUTER Zustand, ein paar Gebrauchsspuren. 26 KHA 9781584885825 Sprache: Englisch Gewicht in Gramm: 1150.

Seller Inventory # 2505592

Bibliographic Details

• Title: Strange functions in real analysis A.B. Kharazishvili. Pure and applied mathematics 272/2.
• Publisher: Boca, Chapman & Hall/CRC
• Publication Date: 2006
• Language: English
• ISBN 10: 1584885823
• ISBN 13: 9781584885825
• Binding: Hardcover
• Edition: 2nd Edition
• Weight: 1150 grams
• Seller catalogs:
  • SA MATHEMATIK

About this title

Synopsis

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.

Review

"The book is written with clear and understandable language and its accessible even for graduate students." -- Zentralblatt fur Mathematik, 2000

"...devised to be a handbook for analysts but it can also be useful to the investigators of structural problems." -- Chem. Anal