Real Analysis: Modern Techniques and Their ApplicationsThis book covers the subject matter that is central to mathematical analysis: measure and integration theory, some point set topology, and rudiments of functional analysis. Also, a number of other topics are developed to illustrate the uses of this core material in important areas of mathematics and to introduce readers to more advanced techniques. Some of the material presented has never appeared outside of advanced monographs and research papers, or been readily available in comparative texts. About 460 exercises, at varying levels of difficulty, give readers practice in working with the ideas presented here. |
Contents
Measures | 18 |
Integration | 42 |
Decomposition and Differentiation of Measures | 80 |
Copyright | |
11 other sections not shown
Common terms and phrases
a₁ absolutely continuous B₁ Banach space Borel measure Borel sets bounded called card(X Cauchy Co(X compact Hausdorff space compact sets complete complex measure continuous function Corollary countable define denote dense differential disjoint union distribution E₁ example Exercise exists f₁ finite measure follows Fourier transform function ƒ ƒ is continuous Haar measure hence implies independent inequality integral intervals Lą(µ LCH space Lebesgue measure left Haar measure Lemma Let f linear map locally compact measurable function measure space metric space Moreover neighborhood nonempty nonnegative normed vector space notation o-algebra o-finite open sets operator outer measure pointwise Proposition prove Radon measure random variables regular result satisfies Section sequence signed measure simple functions subspace supp(ƒ Suppose T₁ theory topological space topology uniformly unique X₁ y₁