Halsey Royden, Patrick Fitzpatrick

Real Analysis (Classic Version)

• Broschiertes Buch

Produktbeschreibung

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.

Produktdetails

• Pearson Modern Classics for Advanced Mathematics Series
• Verlag: Pearson
• 4. Aufl.
• Seitenzahl: 528
• Erscheinungstermin: 21. August 2017
• Englisch
• Abmessung: 182mm x 235mm x 32mm
• Gewicht: 100g
• ISBN-13: 9780134689494
• ISBN-10: 0134689496
• Artikelnr.: 47116979

Inhaltsangabe

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