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Real Analysis (Classic Version), 4th edition

  • Halsey Royden
  • Patrick Fitzpatrick
Real Analysis (Classic Version)

ISBN-13: 9780134689494

Includes: Paperback

4th edition

Published by Pearson (February 13th 2017) - Copyright © 2018

Free delivery
$99.99 $79.99
Free delivery
$99.99 $79.99

What's included

  • Paperback

    You'll get a bound printed text.

Overview

This text is designed for graduate-level courses in real analysis.


This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics for a complete list of titles.

 

Real Analysis, 4th Edition, covers the basic material that every graduate student should know in the classical theory of functions of a real variable, measure and integration theory, and some of the more important and elementary topics in general topology and normed linear space theory. This text assumes a general background in undergraduate mathematics and familiarity with the material covered in an undergraduate course on the fundamental concepts of analysis. Patrick Fitzpatrick of the University of Maryland—College Park spearheaded this revision of Halsey Royden’s classic text. 

 

Table of contents

  • PART I: LEBESGUE INTEGRATION FOR FUNCTIONS OF A SINGLE REAL VARIABLE
  • 1. The Real Numbers: Sets, Sequences and Functions
  • 2. Lebesgue Measure
  • 3. Lebesgue Measurable Functions
  • 4. Lebesgue Integration
  • 5. Lebesgue Integration: Further Topics
  • 6. Differentiation and Integration
  • 7. The LΡ Spaces: Completeness and Approximation
  • 8. The LΡ Spaces: Duality and Weak Convergence
  • PART II: ABSTRACT SPACES: METRIC, TOPOLOGICAL, AND HILBERT
  • 9. Metric Spaces: General Properties
  • 10. Metric Spaces: Three Fundamental Theorems
  • 11. Topological Spaces: General Properties
  • 12. Topological Spaces: Three Fundamental Theorems
  • 13. Continuous Linear Operators Between Banach Spaces
  • 14. Duality for Normed Linear Spaces
  • 15. Compactness Regained: The Weak Topology
  • 16. Continuous Linear Operators on Hilbert Spaces
  • PART III: MEASURE AND INTEGRATION: GENERAL THEORY
  • 17. General Measure Spaces: Their Properties and Construction
  • 18. Integration Over General Measure Spaces
  • 19. General LΡ Spaces: Completeness, Duality and Weak Convergence
  • 20. The Construction of Particular Measures
  • 21. Measure and Topology
  • 22. Invariant Measures

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