Real Analysis (Classic Version), 4th edition

Published by Pearson (February 13, 2017) © 2018

  • Halsey L. Royden
  • Patrick M. Fitzpatrick
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This text is designed for graduate-level courses in real analysis.

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.

  • 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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