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Real Analysis

Real Analysis

Author(s):
  • Halsey Royden
    • Author: Halsey Royden
    • ISBN:9789332551589
    • 10 Digit ISBN:9332551588
    • Price:Rs. 650.00
    • Pages:544
    • Imprint:Pearson Education
    • Binding:Paperback
    • Status:Available


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    Real Analysis, Fourth 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. Patrick Fitzpatrick of the University of Maryland—College Park spearheaded this revision of Halsey Royden's classic text

    Table of Content

    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

    Salient Features

    • Independent, modular chapters give instructors the freedom to arrange the material into a course according that suits their needs. A chart in the text gives the essential dependencies.
    • Content is divided into three parts:
    o Part 1: Classical theory of functions, including the classical Banach spaces
    o Part 2: General topology and the theory of general Banach spaces
    o Part 3: Abstract treatment of measure and integration
    • Throughout the text, an understanding of the linkages between the three parts is fostered. The expanded collection of problems range from those that confirm understanding of basic results and ideas to those that are quite chal¬lenging; many problems foreshadow future developments.