Real analysis 
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Review: Real Analysis
User Review  Thomas  GoodreadsIf I can, I would give it one and a half. I read only seven chapters of the book.The merits are that it is a slow introduction to Lebesgue measure and integration. On the other hand, a lot of non ... Read full review
Review: Real Analysis
User Review  Imran Qureshi  Goodreadsthis proof is trivial...is the main text of the book. was left confused and baffled a bit more than most math books Read full review
Contents
Prologue to the Student  1 
The Real Number System  29 
The Lebesgue Integral  73 
Copyright  
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Common terms and phrases
absolutely continuous Baire measure Baire set Banach space Borel equivalence Borel measure Borel sets Borel subset bounded linear functional called Cauchy sequence closed sets cluster point compact Hausdorff space compact space continuous function continuous realvalued function Convergence Theorem countable collection countably compact definition denote element finite measure finite number following proposition function defined function f given Hausdorff space Hence homeomorphism If/is implies integrable function Lebesgue measure Lemma Let f Let/be lim xn locally compact measurable function measurable sets measure space measure zero monotone natural numbers nonempty nonnegative measurable function normed linear space onetoone open intervals open set outer measure point of closure Problem Proof ralgebra containing rfinite rational numbers semicontinuous sequence of measurable sequence xn set containing set function set of finite set of measure set of real Show simple functions subspace topological space topological vector space unique