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    Function integrable proof

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    Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].

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    Please see the attachment.

    Let f: [a,b] mapped onto Reals be a nonnegative function that is integrable over [a,b]. Then the integral from a to b of f = 0 if and only if greatest lower bound of f (I) = 0 for each open interval I in [a,b].

    Proof. By the hypothesis, we know that for all .
    If , ...

    Solution Summary

    This describes a function mapped onto the real numbers that is integrable, and uses this fact to prove a related function is integrable.

    $2.49

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