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Math Help - Show this set if measurable

  1. #1
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    Feb 2010
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    Show this set is measurable

    Let f be a function from  R^n to  R^+ such that:

    Uf = {(x,y): 0 < y< f(x)} is a measurable set in  R^{n+1}

    The following I am copying exactly as I have it in my notes:

    Suppose a > 1

    Let  S_d = {(x, y-a): f(x) > a, 0 < y < (f(x) -a)/d and 0 < y < 1}

    Show  S_d is measurable for all d>0

    I think it's because:

     S_d is a translation Uf  \cap ((a, a+d)X  R^n ), which is measurable.

    Any thoughts
    Last edited by southprkfan1; April 7th 2010 at 03:41 PM.
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