  We introduce a new `geometric realization' of an (abstract) simplicial
complex, inspired by probability theory. This space (and its completion) is a
metric space, which has the right (weak) homotopy type, and which can be
compared with the usual geometric realization through a natural map, which has
probabilistic meaning : it associates to a random variable its probability mass
function. This `probability map' function is proved to be a (Serre) fibration
and a (weak) homotopy equivalence.

Algebraic Topology;Probability