Continuous functions on the space of probabilities

Abstract:

Weiss and Dubins discovered that any continuous function $g(P)$ on the space of probabilities $\mathcal {P}$ of a compact Hausdorff space $K$ is of the form $\smallint f\;d{P^\infty }$ for some continuous function $f$ on ${K^\infty }$. A short proof is given here.