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If for n-dimensions f>=0 , prove the integral of f >=0

  1. Mar 8, 2015 #1
    1. The problem statement, all variables and given/known data

    2. Relevant equations

    3. The attempt at a solution
    a) The furthest I have got to understanding the solution is that I need to find a way to show that sup(f(x1,x2,...,xn) >= 0. Intuitively and graphically I can see why the statement is obvious, I'm just having a hard time starting to write the proof...
  2. jcsd
  3. Mar 8, 2015 #2


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    If ##f(x_1,..x_n) \ge 0## then it's pretty obvious ##sup(f(x_1,..x_n)) \ge 0##. If you don't have a convenient theorem like if ##f \ge g## then ##\int f \ge \int g##, then you might have to use the definition of the integral.
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