Title: Continuous version of the Choquet integral representation theorem
Abstract: Let $E$ be a locally convex topological Hausdorff space, $K$ a nonempty compact convex subset of $E$, $\mu$ a regular Borel probability measure on $E$ and $\gamma >0$. We say that the measure $\mu$ $\gamma $-represents a point $x\in K$ if $\sup_{\| f\|\le