| Description |
1 online resource |
| Contents |
Cover; Title Page; Copyright Page; Dedication; Authorâ#x80;#x99;s Foreword; Table of Contents; Chapter I: Cardinal Numbers; Sets; Functions and Relations; Equivalent Sets; Cardinals; Problems and Questions; Chapter II: Ordinal Numbers; Ordered Sets; Well-ordered Sets and Ordinals; Applications of Zornâ#x80;#x99;s Lemma; The Continuum Hypothesis; Problems and Questions; Chapter III: The Riemann-Stieltjes Integral; Functions of Bounded Variation; Existence of the Riemann-Stieltjes Integral; The Riemann-Stieltjes Integral and Limits; Problems and Questions; Chapter IV: Abstract Measures |
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Algebras and Ï#x83;-algebras of SetsAdditive Set Functions and Measures; Properties of Measures; Problems and Questions; Chapter V: The Lebesgue Measure; Lebesgue Measure on Rn; The Cantor Set; Problems and Questions; Chapter VI: Measurable Functions; Elementary Properties of Measurable Functions; Structure of Measurable Functions; Sequences of Measurable Functions; Problems and Questions; Chapter VII: Integration; The Integral of Nonnegative Functions; The Integral of Arbitrary Functions; Riemann and Lebesgue Integrals; Problems and Questions; Chapter VIII: More About L1; Metric Structure of L1 |
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The Lebesgue Differentiation TheoremProblems and Questions; Chapter IX: Borel Measures; Regular Borel Measures; Distribution Functions; Problems and Questions; Chapter X: Absolute Continuity; Vitaliâ#x80;#x99;s Covering Lemma; Differentiability of Monotone Functions; Absolutely Continuous Functions; Problems and Questions; Chapter XI: Signed Measures; Absolute Continuity; The Lebesgue and Radon-Nikodým Theorems; Problems and Questions; Chapter XII: LP Spaces; The Lebesgue LP Spaces; Functionals on Lp; Weak Convergence; Problems and Questions; Chapter XIII: Fubiniâ#x80;#x99;s Theorem; Iterated Integrals |
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Convolutions and Approximate IdentitiesAbstract Fubini Theorem; Problems and Questions; Chapter XIV: Normed Spaces and Functionals; Normed Spaces; The Hahn-Banach Theorem; Applications; Problems and Questions; Chapter XV: The Basic Principles; The Baire Category Theorem; The Space B(X, Y); The Uniform Boundedness Principle; The Open Mapping Theorem; The Closed Graph Theorem; Problems and Questions; Chapter XVI: Hilbert Spaces; The Geometry of Inner Product Spaces; Projections; Orthonormal Sets; Spectral Decomposition of Compact Operators; Problems and Questions; Chapter XVII: Fourier Series |
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The Dirichlet KernelThe Fejér Kernel; Pointwise Convergence; Chapter XVIII: Remarks on Problems and Questions; Index |
| Summary |
A modern introduction to the theory of real variables and its applications to all areas of analysis and partial differential equations. The book discusses the foundations of analysis, including the theory of integration, the Lebesque and abstract integrals, the Radon-Nikodym Theorem, the Theory of Banach and Hilbert spaces, and a glimpse of Fourier series. All material is presented in a clear and motivational fashion |
| Notes |
Includes index |
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Online resource; title from PDF title page (EBSCO, viewed March 15, 2018) |
| Subject |
Functions of real variables.
|
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MATHEMATICS -- Calculus.
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MATHEMATICS -- Mathematical Analysis.
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Functions of real variables
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| Form |
Electronic book
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| ISBN |
9780429493171 |
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0429493177 |
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