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A Double Integral Proof

  1. Jul 13, 2007 #1
    Show that if f is defined on a rectangle R and double integral of f on R
    exists, then f is necessarily bounded on R.
     
  2. jcsd
  3. Jul 13, 2007 #2
    If the function is defined on the rectangle the I can't see how it could be unbounded there. Do you mean almost everywhere defined? In the second case, the statement is wrong. Try

    [tex]\int_0^1\int_0^1 \frac{y}{\sqrt{x}}dxdy[/tex]
     
  4. Jul 13, 2007 #3

    mathman

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    Science Advisor

    This will be true if you define the integral in terms of ordinary Riemann or Darboux definition. There are more general definitions where boundedness is not required.
     
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