Hi, I have a compact (under weak convergence) convex set which is a subset of the space of real valued measures on a compact subset of \Re^n. I know the extreme points of this set, and want to write the Choquet representation.
Is d(a,b)= \int |a-b|, where a,b are measures the right metric? (Is it a complete metric?) If so, is this all I need?
Is there a good reference for this stuff, at a somewhat elementary level. I'm a novice at measure theory.