  We consider the space $M(X)$ of separable measures on the Borel
$\sigma$-algebra ${\cal B}(X)$ of a metric space $X$. The space $M(X)$ is
furnished with the Kantorovich-Rubinshte\u{i}n metric known also as the
``Hutchinson distance''. We prove that $M(X)$ is complete if and only if $X$ is
complete. We consider applications of this theorem in the theory of
self-similar fractals.
