This is the classic introductory graduate text. Heart of the book is measure theory and Lebesque integration.This is the classic introductory graduate text. Heart of the book is measure theory and Lebesque integration.Read Less
New. This Fourth Edition of Real Analysis preserves the goal and general structure of its venerable predecessors to present the measure theory, integration theory, and functional analysis that a modern analyst needs to know. New to this Edition: This edition contains 50% more exercises than the previous edition. Fundamental results, including Egoroff's Theorem and Urysohn's Lemma are now proven in the text. The Borel-Cantelli Lemma, Chebychev's Inequality, rapidly Cauchy sequences, and the continuity properties possessed both by measure and the integral are now formally presented in the text along with several other concepts. Contents Preface 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 Lp Space: Completeness and Approximation 8. The Lp Space: Duality and Weak Convergence II Abstract Spaces: Metric, Topological, Banach, and Hilbert Spaces 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 III Measure and Integration: General Theory 17. General Measure Spaces: Their Properties and Construction 18. Integration Over General Measure Spaces 19. General LP Spaces: Completeness, Duality, and Weak Convergence 20. The Construction of Particular Measures 21. Measure and Topology 22. Invariant Measures. Bibliography " Index. Printed Pages: 520. 18 x 24 cm.
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