  We propose some axioms for hierarchical clustering of probability measures
and investigate their ramifications. The basic idea is to let the user
stipulate the clusters for some elementary measures. This is done without the
need of any notion of metric, similarity or dissimilarity. Our main results
then show that for each suitable choice of user-defined clustering on
elementary measures we obtain a unique notion of clustering on a large set of
distributions satisfying a set of additivity and continuity axioms. We
illustrate the developed theory by numerous examples including some with and
some without a density.
