1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

One integral inequality

  1. Mar 8, 2008 #1
    Let X be a measure space, and [itex]f:X\times X\to [0,\infty[[/itex] some integrable function. Is the following inequality always true,

    \int\limits_{X} dx\;f(x,x)\; \leq\; \sup_{x_1\in X} \int\limits_{X} dx_2\; f(x_1,x_2) ?
    Last edited: Mar 8, 2008
  2. jcsd
  3. Mar 8, 2008 #2


    User Avatar
    Science Advisor
    Gold Member

    No. Let f(x,y)=sinxsiny for 0<=x,y,<=2pi and zeo otherwise. The left integral is pi, while the right integral is 0.
  4. Mar 8, 2008 #3
    I see.

    f:[0,2\pi]\times [0,2\pi]\to [0,\infty[,\quad f(x,y) = \sin(x)\sin(y) + 1

    gives a counter example that satisfies the original conditions.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: One integral inequality
  1. Integration Inequality (Replies: 3)