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Thread: Show this set if measurable

  1. #1
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    Show this set is measurable

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

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

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

    Suppose a > 1

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

    Show $\displaystyle S_d $ is measurable for all d>0

    I think it's because:

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

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