  Measure homology was introduced by Thurston in order to compute the
simplicial volume of hyperbolic manifolds. Berlanga endowed measure homology
with a structure of graded locally convex (possibly non-Hausdorff) topological
vector space. In this note we completely characterize Berlanga's topology on
measure homology of CW-complexes, showing in particular that it is Hausdorff.
This answers a question posed by Berlanga.
