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 February 24th, 2014, 03:39 AM #1 Member   Joined: Aug 2012 Posts: 32 Thanks: 0 Lebesgue integration question Lebesgue integral question: Consider measure space with a summable function. I want to show that if then a.e. and therefore a.e. My proposed proof is as follows: Assume that for some . Since is positive measurable function it follows that it is the limit of an increasing sequence of simple functions which I will show as : Using Beppoi Levi I know that the limit of the integral is the integral of the limit which gives the following: This is only possible if for any we have . for all and it follows that either or . Since we assumed that is nonzero for some it follows that there is some where therefore there must be some such that and which gives for . It follows that a.e. and therefore a.e. Is this proof fine? Thanks for assistance. Tags integration, lebesgue, question Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Fabion Real Analysis 0 March 20th, 2014 09:10 AM Fabion Real Analysis 0 March 10th, 2014 03:48 AM thamy_271091 Calculus 9 December 7th, 2012 06:34 AM mathabc Real Analysis 0 June 23rd, 2011 10:11 PM aptx4869 Real Analysis 5 May 7th, 2008 06:44 AM

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