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February 9th, 2009, 02:04 PM  #1 
Newbie Joined: Feb 2009 Posts: 2 Thanks: 0  Give an example of a sequence of integrable functions that..
Can you guys think of any exampleS? Give an example of a sequence of integrable functions {fn} (going from 1 to infinity) on [0,1] that converges pointwise to a non integrable function f:[0,1]>R 
February 9th, 2009, 04:15 PM  #2 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Give an example of a sequence of integrable functions that..
Riemann or Lebesgue integrable? If it's Riemann, consider defined by Then, but as converges pointwise to the function which is not Riemann integrable (but is Lebesgue integrable). If you want a series of functions that converge pointwise to a nonLebesgueintegrable function, then it's too late for my brain to work sufficiently... 
February 9th, 2009, 04:32 PM  #3 
Senior Member Joined: May 2008 From: York, UK Posts: 1,300 Thanks: 0  Re: Give an example of a sequence of integrable functions that..
OK, maybe it's not too late... consider given by Then and converges pointwise to the function which is not integrable on [0,1]. 

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