This question arised in my last math class: If a sequence of functions [tex]f_n[/tex] uniformly converges 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.