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Math Help - zero content

  1. #1
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    zero content

    Let f:[a,b]-> R be an integrable function.
    Show that the graph of f in R^2 has zero content.
    (hint: given a partition P of [a,b], interpret Spf-spf as a sum of areas of rectangles that cover the graph of f. )
    Not sure where to start, any help?
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Hint:

    f integrable in [a,b] iff for every \epsilon>0 there exists a partition P of [a,b] such that U(P,f)-L(P,f)<\epsilon.
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