Real Analysis (Classic Version)

by Halsey Royden, Patrick Fitzpatrick

Overview

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. It 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.

This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price.

Product Details

ISBN-13:	9780134689494
Publisher:	Pearson Education
Publication date:	02/13/2017
Series:	Pearson Modern Classics for Advanced Mathematics Series
Edition description:	New Edition
Pages:	528
Product dimensions:	7.00(w) x 9.00(h) x 1.10(d)

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 L ^Ρ Spaces: Completeness and Approximation
• 8. The L ^Ρ 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 L
  
  ^Ρ Spaces: Completeness, Duality and Weak Convergence
• 20. The Construction of Particular Measures
• 21. Measure and Topology
• 22. Invariant Measures