Real Analysis
Series: Oxford Graduate Texts in Mathematics;
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56 936 Ft
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Product details:
- Publisher OUP Oxford
- Date of Publication 27 October 2016
- ISBN 9780198790426
- Binding Hardback
- No. of pages320 pages
- Size 240x162x21 mm
- Weight 666 g
- Language English 0
Categories
Short description:
Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. The book is aimed at graduate students of mathematics and related disciplines wishing to learn the basics and techniques of Real Analysis with reasonable ease.
MoreLong description:
Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. This concise and friendly book is written for early graduate students of mathematics or of related disciplines hoping to learn the basics of Real Analysis with reasonable ease. The essential role of Real Analysis in the construction of basic function spaces necessary for the application of Functional Analysis in many fields of scientific disciplines is demonstrated with due explanations and illuminating examples.
After the introductory chapter, a compact but precise treatment of general measure and integration is taken up so that readers have an overall view of the simple structure of the general theory before delving into special measures. The universality of the method of outer measure in the construction of measures is emphasized because it provides a unified way of looking for useful regularity properties of measures. The chapter on functions of real variables sits at the core of the book; it treats in detail properties of functions that are not only basic for understanding the general feature of functions but also relevant for the study of those function spaces which are important when application of functional analytical methods is in question. This is then followed naturally by an introductory chapter on basic principles of Functional Analysis which reveals, together with the last two chapters on the space of p-integrable functions and Fourier integral, the intimate interplay between Functional Analysis and Real Analysis. Applications of many of the topics discussed are included to motivate the readers for further related studies; these contain explorations towards probability theory and partial differential equations.
The book is largely self-contained, including not only the basic concepts of measure theory that underlie integration, but also the linear analysis that provides the multidimensional spaces context... Recommended.
Table of Contents:
Introduction and Preliminaries
A Glimpse of Measure and Integration
Construction of Measures
Functions of Real Variables
Basic Principles of Linear Analysis
Lp Spaces
Fourier Integral and Sobolev Space Hs
Postscript
Real Analysis
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