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

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

English | 2016 | ISBN: 1634850211 | 354 Pages | PDF | 3.41 MB

This book is intended for readers who have had a course in theory of functions, isodifferential calculus and it can be used for a senior undergraduate course.

Chapter 1 deals with the infinite sets. We introduce the main operations on the sets. They are considered the one-to-one correspondences, the denumerable sets and the non-denumerable sets, and their properties.

In Chapter 2 are introduced the point sets. They are defined the limit points, the interior points, the open sets, the closed sets. They are considered the structure of the bounded open and the closed sets. Also, they are given some of their main properties.

In Chapter 3 are studied the measurable sets. They are defined and deducted the main properties of the measure of a bounded open set, a bounded closed set, the outer and the inner measures of a bounded set.

Chapter 4 is devoted to the theory of the measurable iso-functions. They are considered the main classes of the measurable iso-functions and they are deducted their properties.

In Chapter 5 is defined the Lebesgue iso-integral of a bounded iso-function. They are given its main properties.

In Chapter 6 are studied the square iso-summable iso-functions, the iso-orthogonal systems, the iso-spaces Lp and lp, p > 1.

The Stieltjes iso-integral and its properties are investigated in Chapter 7.

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