Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    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.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook