書誌事項

Real analysis

H.L. Royden, P.M. Fitzpatrick

(Pearson modern classic)

Prentice Hall/Pearson, c2018

4th ed, updated printing

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注記

Includes bibliographical references (p. 497-498) and index

内容説明・目次

内容説明

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.

目次

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

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