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February 9th, 2009, 03:04 PM   #1
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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
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February 9th, 2009, 05:15 PM   #2
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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 non-Lebesgue-integrable function, then it's too late for my brain to work sufficiently...
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February 9th, 2009, 05:32 PM   #3
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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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