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Math Help - Integrable function

  1. #1
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    Integrable function

    Could someone give me a hand on this problem? I want to show that a bounded function f: [a,b] \rightarrow R having a convergent sequence of discontinuous points is Riemann integrable.
    I was able to show that that a function bounded function having finitely many discontinuous points is Riemann integrable.
    I think I need to come up with a partition P such that U(P,f)-L(P,f) < \epsilon for this problem.
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  2. #2
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    If you can do a similar problem for a finite collection of discontinuities, then this problem requires almost the same proof. Because the sequence of discontinuities converges, almost all of the discontinuities are in a cell of any partition containing the limit point as an interior point.
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