Coherent Distributions on the Square

Let C denote the family of coherent distributions on [0,1]^2, i.e. all those probability measures m for which there exists a random
vector (X,Y)~m such that X=P(E|G), Y=P(E|H) a.s. for some event E and sigma fields G,H. During the talk, we will:

1) examine the set of extreme points of C and provide its general characterisation;
2) derive several structural properties of extremal coherent measures with finite support,
3) using 1) and 2), analyse the behaviour of sup_C E|X-Y|^N, for N going to infinity.