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Math Help - Minimum sum equals sum of minima?

  1. #1
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    Minimum sum equals sum of minima?

    Hello everyone!

    If we have functions, f1(t), f2(t), etc. all positive in our observation window, plus:
    f_1(t) > f_2(t) > ... > f_N(t) for all a<t<b, does it follow that:
    \int ^b _a f_1(t)dt > \int ^b _a f_2(t)dt > ... > \int ^b _a f_N(t)dt?

    i.e. is the saying "minimum sum equals sum of minima" correct here?


    Thanks!
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  2. #2
    A Plied Mathematician
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    Re: Minimum sum equals sum of minima?

    It does follow from a basic theorem in analysis. That is, the theorem holds when N = 2, and I think you could induct on N.
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