Real and Complex AnalysisThis is an advanced text for the one- or two-semester course in analysis taught primarily to math, science, computer science, and electrical engineering majors at the junior, senior or graduate level. The basic techniques and theorems of analysis are presented in such a way that the intimate connections between its various branches are strongly emphasized. The traditionally separate subjects of 'real analysis' and 'complex analysis' are thus united in one volume. Some of the basic ideas from functional analysis are also included. This is the only book to take this unique approach. The third edition includes a new chapter on differentiation. Proofs of theorems presented in the book are concise and complete and many challenging exercises appear at the end of each chapter. The book is arranged so that each chapter builds upon the other, giving students a gradual understanding of the subject. This text is part of the Walter Rudin Student Series in Advanced Mathematics. |
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Contents
Abstract Integration | 5 |
Positive Borel Measures | 34 |
Elementary Hilbert Space Theory | 79 |
Copyright | |
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2π π A₁ assume B₁ Banach algebra Banach space Blaschke product Borel measure Borel set bounded linear functional Cauchy compact set compact subset completes the proof complex function complex measurable complex numbers constant contains continuous function converges uniformly convex countable D₁ defined Definition dense differentiable disc disjoint entire function Exercise exists finite follows Fourier transform function f ƒ and g harmonic function Hausdorff space Hence Hilbert space holds holomorphic functions implies inequality Lebesgue measure Lemma mapping measurable function measure space metric space o-algebra one-to-one open set plane Poisson integral polynomials positive measure proof of Theorem properties Prove that ƒ real number region satisfies semicontinuous sequence shows simply connected subspace Suppose ƒ supremum Theorem Suppose u₁ union vector space zero Σπί