Real AnalysisMacmillan, 1988 - 444 sider Dealing with measure theory and Lebesque integration, this is an introductory graduate text. |
Indhold
Prologue to the Student | 1 |
The Real Number System | 31 |
The Lebesgue Integral | 75 |
Copyright | |
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A₁ absolutely continuous algebra axiom B₁ Baire measure Baire sets Borel measure Borel sets called Cauchy sequence closed set compact Hausdorff space compact set complete metric space continuous function continuous map continuous real-valued function convex Corollary countable collection definition dense disjoint E₂ element equicontinuous equivalent finite measure finite number following proposition func function f ƒ and g given Hausdorff space Hence Hint homeomorphism inequality inner regular intersection isomorphic L₁ Lebesgue measure Lemma Let f Let ƒ Let G locally compact Hausdorff measurable function measurable sets measure space measure zero monotone natural numbers nonempty nonnegative measurable function o-algebra o-finite open covering open intervals open set open subset outer measure point of closure Problem Proof Prove Proposition real numbers set function set of measure simple functions subspace tion topological space topologically equicontinuous union unique x₁