Alexander Kharazishvili

Strange Functions in Real Analysis

• Broschiertes Buch

Produktbeschreibung

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. Finally, he considers examples of functions whose existence cannot be established without the help of addition set-theoretical axioms. This edition includes five new chapters that provide more information on the structure of strange functions, nearly 70 new exercises that extend the discussions within the text, and a significantly expanded list of reference that incorporates recent works.

Produktdetails

• Verlag: Taylor & Francis Ltd (Sales)
• 2nd edition
• Seitenzahl: 432
• Erscheinungstermin: 5. September 2019
• Englisch
• Abmessung: 226mm x 152mm x 23mm
• Gewicht: 567g
• ISBN-13: 9780367391461
• ISBN-10: 0367391465
• Artikelnr.: 57733506

Autorenporträt

Kharazishvili, Alexander

Inhaltsangabe

Introduction: Basic Concepts. Cantor and Peano Type Functions. Functions of
First Baire Class (new). Semicontinuous Functions which are not Countably
Continuous (new). Singular Monotone Functions. Everywhere Differentiable
Nowhere Monotone Functions. Nowhere Approximately Differentiable Functions.
Blumberg's Theorem and Sierpinski-Zygmund Function. 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.