This question arised in my last math class:(adsbygoogle = window.adsbygoogle || []).push({});

If a sequence of functions [tex]f_n[/tex]uniformlyconverges to some [tex]f[/tex] on [tex](a, b)[/tex] (bounded) and all [tex]f_n[/tex] are integrable on [tex](a, b)[/tex], does this imply that [tex]f[/tex] is also integrable on [tex](a, b)[/tex] ??

([tex]f_n[/tex] do not necessarily have to be continous, if they were, the answer would be obvious)

Note: It is not certain, which type of integral is meant, it can be Newton, Riemann or Lebesgue. Let me please know if the answer depends on which type of integral is used.

- If it is true, could you please tell me where (on www) I might find a proof??

- If it is not true, could you please show me a sequence for which it is not true??

Thanks a lot, H.

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# Uniform convergence of integrable functions

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