Posted by J. Holmer on November 20, 2007, 4:41 pm, in reply to "Problems 4, 7 "
Board Administrator
7. My first inclination for this problem is to use Fubini's theorem; in particular Cor. 3.8. First reduce to the case f>=0. Define the sets
A_\epsilon = { (x,y) | 0 <= y <= (1-\epsilon)f(x) }
B_\epsilon = { (x,y) | 0 <= y <= (1+\epsilon)f(x) }
Then \Gamma \subset (B_\epsilon - A_\epsilon) for all \epsilon, and in fact
\Gamma = \intersection_n (B_{1/n}-A_{1/n})
4/19. Use Fubini's theorem.
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