integrating the minimum metric
Hello, I tried this in analysis but maybe it is a more topological question. If given a function f on R such that \int_R f(x)dx = 1 and is decreasing and 1lipschitz, show that
the function g(y) = min{x,f(x)} where y = xf(x) and x>=0, also satisfies \int_Y g(y)dy=1. I really would appreciate any observations. The transformation of the Domain is 11 right? so what else is required to have integral unity of g also? I have some other info that may or may not help: f(x) = g(y) 1/2y +1/2y, x=g(y)+1/2y +1/2y. Thank you 
Re: integrating the minimum metric
Quote:

Re: integrating the minimum metric
I refer you to the bibliography item in my thesis:
1. B.F. Logan and L.A. Shepp. A Variational Problem for Random Young Tableaux. Ad vances in Mathematics, 26, 1977, 206222. The problem is solved now using lebesgue measure... 
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