A Course of Higher Mathematics
Integration and Functional Analysis, Volume 5
- 650 pages
- English
- PDF
- Only available on web
A Course of Higher Mathematics
Integration and Functional Analysis, Volume 5
About This Book
A Course of Higher Mathematics, Volume V focuses on the theory of integration and elements of functional analysis. This book is organized into five chapters. Chapter I discusses the theory of the classical Stieltjes integral and space C of continuous functions, while Chapter II deals with the foundations of the metric theory of functions of a real variable and Lebesgue-Stieltjes integral. The theory of completely additive set functions and case of the one-dimensional Hellinger integral are analyzed in Chapter III. Chapter IV contains an exposition of the foundations of the general theory of metric and normed spaces. The general theory of Hilbert space is covered in Chapter V. This volume is suitable for engineers, physicists, and students of pure mathematics.
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Table of contents
- Front Cover
- A Course of Higher Mathematics
- Copyright Page
- Table of Contents
- INTRODUCTION
- PREFACE
- CHAPTER I. THE STIELTJES INTEGRAL
- CHAPTER II. SET FUNCTIONS AND THE LEBESGUE INTEGRAL
- CHAPTER III. SET FUNCTIONS. ABSOLUTE CONTINUITY. GENERALIZATION OF THE INTEGRAL
- CHAPTER IV. METRIC AND NORMED SPACES
- CHAPTER V. HILBERT SPACE
- INDEX