On the existence of extreme coherent distributions with no atoms

I will talk about extreme points of C, the family of all two-variate coherent distributions on [0,1]^2. It is well-known that the set C is convex and weak∗ compact, and all extreme points of C are supported on sets of Lebesgue measure zero. Conversely, examples of extreme coherent measures, with a finite or countable infinite number of atoms, have been successfully constructed in the literature.

The main purpose of this talk is to bridge the natural gap between those two results: we provide an example of extreme coherent distribution with an uncountable support and with no atoms. Our argument is based on classical tools and ideas from the dynamical systems theory.