Foundations of Iso-Differential Calculus

Volume 6: Theory of Iso-Functions of a Real Iso-Variable

Svetlin Georgiev (Autor)

Buch | Hardcover

350 Seiten

2016
Nova Science Publishers Inc (Verlag)
978-1-63485-021-6 (ISBN)

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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 Lp and l p, p > 1 are studied. The Stieltjes iso-integral and its properties are investigated in Chapter Seven.

Svetlin Georgiev (born 1974) is a Bulgarian mathematician working in areas of ordinary differential equations, partial differential equations, stochastic differential equations, Clifford algebras and Clifford analysis. He is currently a Professor at Sofia University (Bulgaria) and Sorbonne University (Paris, France). Svetlin Georgiev is Editor -in- Chief of the journal Clifford Analysis, Clifford Algebras and their Applications. He serves on the advisory board of 5 further journals. He has comprehensive teaching experience in different levels for about 15 years.

Preface; Infinite Sets; Point Sets; Measurable Sets; Measurable Iso-functions; The Lebesgue Iso-integral of a Bounded Iso-function; Square-iso-summable Iso-functions; The Stieltjes Iso-integral; Appendix; Index.

Erscheinungsdatum	05.04.2016
Verlagsort	New York
Sprache	englisch
Maße	180 x 260 mm
Gewicht	786 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-63485-021-1 / 1634850211
ISBN-13	978-1-63485-021-6 / 9781634850216
Zustand	Neuware