Showing that ∫ X log ( f ) d μ ≤ μ ( X...
Showing that given that for positive without using Jensen's inequality.
We weren't presented with Jensen's inequality, but with Fubini's Theorem and another theorem which is:
in a finite measure space satisfies
At first I thought I should use , and show that if , then
which I can't seem to contradict. Any ideas how this can be shown, without using Jensen's Inequality?