Strange Functions in Real Analysis

ISBN-13: 9780367391461 / Angielski / Miękka / 2019 / 432 str.

Alexander Kharazishvili

Opis

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.

Spis treści

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.

O autorze

Kharazishvili, Alexander