  Given a prior probability density $p$ on a compact set $K$ we characterize
the probability distribution $q_{\delta}^*$ on $K$ contained in a Wasserstein
ball $B_{\delta}(\mu)$ centered in a given discrete measure $\mu$ for which the
relative-entropy $H(q,p)$ achieves its minimum. This characterization gives us
an algorithm for computing such distributions efficiently
