Convergent estimators for the L1-median of a Banach valued random variable

Let E be a separable Banach space, which is the dual of a Banach space F. If X is an E-valued random variable, the set of L-1-medians of X is Argmin(alpha is an element ofE) E[parallel toX - alpha parallel to - parallel toX parallel to]. Assume that this set contains only one element. From any sequence of probability measures {mu (n), n > 1} on E, which converges in law to X, we give two approximating sequences of the LI-median, for the weak* topology induced by F.