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Math Help - Let f be a bounded measurable function on [a,b]...

  1. #1
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    Let f be a bounded measurable function on [a,b]...

    Hi there. I am new here. I am really sorry to ask, but I have been hung up on this problem for a couple of days. I just don't understand what I am supposed to do. Sorry for the lack of Latex, but I think my writing is understandable. My problem is below. Thanks in advance.
    Let f be a bounded measurable function on [a,b]. If A is a measurable subset of [a,b] with lambda(A) = 0, prove that integral of f d(lambda) = 0. (The subscript on the integral is A)
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  2. #2
    Member mabruka's Avatar
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    Hi

    Remember that


    \left |\int_A f d\lambda \right| \leq \int_A |f| d\lambda \leq M \lambda(A) =0

    where |f|\leq M.
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