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Real analysis

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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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Availability

Detail Information

Series Title

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Call Number

515 ROY r

Publisher

New York : Pearson Education., 2010

Collation

xii, 508 hal.; ilus.; 24 cm

Language

English

ISBN/ISSN

9780131437470

Classification

515

Content Type

-

Media Type

-

Carrier Type

-

Edition

Fourth Edition

Subject(s)

functions of real variable
functional analysis
measure theory

Specific Detail Info

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Statement of Responsibility

H.L. Royden dan P.M. Fitzpatrick

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