A Concise Introduction to the Theory of IntegrationDesigned for the full-time analyst, physicist, engineer, or economist, this book attempts to provide its readers with most of the measure theory they will ever need. The author has consistently developed the concrete rather than the abstract aspects of topics treated. The major new feature of this third edition is the inclusion of a new chapter in which the author introduces the Fourier transform. Solutions to all problems are provided. As a self-contained text, this book is excellent for both self-study and the classroom. |
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absolutely continuous addition AgN-1 dw algebra apply assertion assume B-measurable B₁ B₂ bounded C₁ choose clear Clearly compact conclude continuously differentiable Corollary countable define denote Dominated Convergence Theorem E₁ element exact cover Exercise exists Fatou's Lemma Finally finite measure follows function ƒ ƒ and g ƒ dµ ƒ ƒ given Hence Hilbert space Hölder's inequality holds L¹(R L¹(RN L¹(T L¹(u L¹(µ L2 RN L²(RN Lebesgue integral Lebesgue measure Lebesgue's Dominated Convergence let ƒ Let G limn linear LP RN measurable function measure space metric space monotone Moreover mutually disjoint non-empty non-overlapping o-algebra observe obvious open set orthonormal basis particular preceding PROOF prove R-valued rectangle respect result Riemann integrable sequence subspace T₁ uniformly vector µ(dx ΣΣ