Foundations of Iso-Differential Calculus. Volume 6: Theory of Iso-Functions of a Real Iso-Variable

Svetlin G. Georgiev
Sorbonne University, Paris, France
Faculty of Mathematics and Informatics, Department of Differential Equations, Sofia University, Sofia, Bulgaria

Series: Mathematics Research Developments
BISAC: SCI013000

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This book is intended for readers who have had a course in theory of functions, isodifferential calculus and it can also be used for a senior undergraduate course. Chapter One deals with the infinite sets. We introduce the main operations on the sets. They are considered as the one-to-one correspondences, the denumerable sets and the nondenumerable sets, and their properties. Chapter Two introduces the point sets. They are defined as the limit points, the interior points, the open sets, and the closed sets. Also included are the structure of the bounded open and the closed sets, and an examination of some of their main properties. Chapter Three describes the measurable sets. They are defined and deducted as the main properties of the measure of a bounded open set, a bounded closed set, and the outer and the inner measures of a bounded set. Chapter Four is devoted to the theory of the measurable iso-functions. They are defined as the main classes of the measurable iso-functions and their associated properties are defined as well. In Chapter Five, the Lebesgue iso-integral of a bounded iso-function continue the discussion of the book. Their main properties are given. In Chapter Six the square iso-summable iso-functions, the iso-orthogonal systems, the iso-spaces ˆLp and ˆl p, p > 1 are studied. The Stieltjes iso-integral and its properties are investigated in Chapter Seven. (Imprint: Nova)

Preface

Chapter 1. Infinite Sets

Chapter 2. Point Sets

Chapter 3. Measurable Sets

Chapter 4. Measurable Iso-functions

Chapter 5. The Lebesgue Iso-integral of a Bounded Iso-function

Chapter 6. Square-iso-summable Iso-functions

Chapter 7. The Stieltjes Iso-integral

Chapter 8. Appendix

Index

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Chapter 21

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