Re: continuous function bounded by concave function

In article <1160634880.585296.140010@xxxxxxxxxxxxxxxxxxxxxxxxxxx>,
diablo <diablo_rojos2000@xxxxxxxxx> wrote:
Can someone prove the following statement: Given a real-valued
continuous function f on [0,1],f(0)=0, prove that there exists a
concave function g, such that g(x)>=f(x) for all x in [0,1] and g(0) =
0.
A function g is called concave if g(tx + (1-t)y) >= tg(x) + (1-t)g(y)
for all 0<=t<=1 and 0<=x,y<=1.

Hint: consider the convex hull of the graph of f.

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada


.

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