Recent content by pulin816

  1. P

    F is integrable but f^2 is not integrable

    super. I thought proofs had to be more complicated, somehow. Is there any theorem that explains integrability?
  2. P

    Lim fn(x) = f(x) but lim ∫ |f(x)-fn(x)|dx ≠ 0 ?

    oh yeah, my mistake. Thanks!
  3. P

    Lim fn(x) = f(x) but lim ∫ |f(x)-fn(x)|dx ≠ 0 ?

    Thanx LeonhardEuler: I tried coming up with a nother function, what about fn(x) = |1/n| for x ∈ [0, n] and fn(x) = 0 elsewhere in [-infinity, infinity] fn(x) will converge to 0 function uniformly however, while ∫ |fn(x)| dx = 2 for all n in N ?
  4. P

    Lim fn(x) = f(x) but lim ∫ |f(x)-fn(x)|dx ≠ 0 ?

    Homework Statement Hey, I have another questions, I need to find an example of a sequence of integrable functions fn:R -> R, n =1, 2, ... such that lim fn(x) = f(x) (as n -> ∞) but lim ∫ |f(x)-fn(x)|dx ≠ 0 (as n -> ∞) (with integral from - to + infinity) The Attempt at a...
  5. P

    F is integrable but f^2 is not integrable

    Homework Statement Give an example of a sequence of integrable functions f:R -> R such that f is integrable but f^2 is not integrable. Prove your results. The Attempt at a Solution would 1/sqrt(x) for x ∈ [0,1] work? any other suggestions? how would you prove that its does work...