Ábel Farkas (Hebrew University, Jerusalem): Conditional measure on the Brownian path and other random sets

Let $B$ denote the range of the Brownian motion in $R^d$. For a deterministic Borel measure $\nu$ we wish to find a random measure $\mu$ such that the support of $\mu$ is contained in $B$ and the expectation of $\mu$ is $\nu$. We discuss when exactly we can find such a $\mu$.