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... 
All times are GMT 5. The time now is 08:03 PM. 
Powered by vBulletin Copyright ©2000  2014, Jelsoft Enterprises Ltd.
© 2014 Physics Forums