| Description |
1 online resource |
| Series |
Oxford graduate texts in mathematics ; 26 |
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Oxford graduate texts in mathematics ; 26
|
| Contents |
880-01 Cover; Contents; Preface; 1 Introduction and Preliminaries; 1.1 Summability of systems of real numbers; 1.2 Double series; 1.3 Coin tossing; 1.4 Metric spaces and normed vector spaces; 1.5 Semi-continuities; 1.6 The space lp (Z); 1.7 Compactness; 1.8 Extension of continuous functions; 1.9 Connectedness; 1.10 Locally compact spaces; 2 A Glimpse of Measure and Integration; 2.1 Families of sets and set functions; 2.2 Measurable spaces and measurable functions; 2.3 Measure space and integration; 2.4 Egoroff theorem and monotone convergence theorem; 2.5 Concepts related to sets of measure zero |
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880-01 5.4 Separation principles5.5 Complex form of Hahn-Banach theorem; 5.6 Hilbert space; 5.7 Lebesgue-Nikodym theorem; 5.8 Orthonormal families and separability; 5.9 The space L2[-π, π]; 5.10 Weak convergence; 6 Lp Spaces; 6.1 Some inequalities; 6.2 Signed and complex measures; 6.3 Linear functionals on Lp; 6.4 Modular distribution function and Hardy-Littlewood maximal function; 6.5 Convolution; 6.6 The Sobolev space Wk, p (Ω); 7 Fourier Integral and Sobolev Space Hs; 7.1 Fourier integral for L1 functions; 7.2 Fourier integral on L2; 7.3 The Sobolev space Hs |
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4.1 Lusin theorem4.2 Riemann and Lebesgue integral; 4.3 Push-forward of measures and distribution of functions; 4.4 Functions of bounded variation; 4.5 Riemann-Stieltjes integral; 4.6 Covering theorems and differentiation; 4.7 Differentiability of functions of a real variable and related functions; 4.8 Product measures and Fubini theorem; 4.9 Smoothing of functions; 4.10 Change of variables for multiple integrals; 4.11 Polar coordinates and potential integrals; 5 Basic Principles of Linear Analysis; 5.1 The Baire category theorem; 5.2 The open mapping theorem; 5.3 The closed graph theorem |
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7.4 Weak solutions of the Poisson equation7.5 Fourier integral of probability distributions; Postscript; Bibliography; List of Symbols; Index |
| Summary |
Real Analysis is indispensable for in-depth understanding and effective application of methods of modern analysis. The book is aimed at graduate students of mathematics and related disciplines wishing to learn the basics and techniques of Real Analysis with reasonable ease |
| Bibliography |
Includes bibliographical references and index |
| Notes |
Vendor-supplied metadata |
| Subject |
Mathematical analysis.
|
|
MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Mathematical analysis.
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| Form |
Electronic book
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| ISBN |
0192507656 |
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9780192507655 |
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