Results 1 to 3 of 3

Math Help - contradict fubin's theorem

  1. #1
    Newbie
    Joined
    Oct 2011
    Posts
    8

    contradict fubin's theorem

    can anyone give an example of a function f(x,y) for which fubini's theorem is not valid.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,340
    Thanks
    21

    Re: contradict fubin's theorem

    This is taken from Stewart's Calculus book

    \int_0^1 \!\!\! \int_0^1 \dfrac{x-y}{(x+y)^3}\,dx\,dy and \int_0^1 \!\!\! \int_0^1 \dfrac{x-y}{(x+y)^3}\,dy\,dx.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,325
    Thanks
    1296

    Re: contradict fubin's theorem

    Nice example! Easy to integrate both sides and see they are not the same. I wouldn't have thought such an example would be so simple.

    Of course, it doesn't "contradict Fubini's theorem". Fubini's theorem does not apply because integral does not satisfy the hypotheses.

    Saurabmtz, Fubini's theorem requires that the integrand be continous on a\le x\le b, c\le y\le d where a, b, c, and d are the limits on the appropriate integrals. This integrand is not continuous at (0, 0).
    Last edited by HallsofIvy; October 7th 2011 at 10:37 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. contradict lagrange's multiplier identity
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 17th 2011, 11:05 AM
  2. fubin'si theoram for a discontinous function
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 12th 2011, 11:24 AM
  3. Replies: 2
    Last Post: February 23rd 2011, 01:10 PM
  4. Do these texts contradict eachother?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 4th 2009, 11:26 AM
  5. Do these texts contradict eachother?
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: November 4th 2009, 09:12 AM

Search Tags


/mathhelpforum @mathhelpforum