  A compact metric space $(X, \rho)$ is given. Let $\mu$ be a Borel measure on
$X$. By $r$-cluster we mean a measurable subset of $X$ with diameter at most
$r$. A family of $k$ $2r$-clusters is called a $r$-cluster structure of order
$k$ if any two clusters from the family are separated by a distance at least
$r$. By measure of a cluster structure we mean a sum of clusters measures from
the cluster structure. Using the Blaschke selection theorem one can prove that
there exists a cluster structure $\mathcal{X}^*$ of maximum measure. We study
dependence $\mu(\mathcal{X}^*)$ on distance distribution. The main issue is to
find restrictions for distance distribution which guarantee that
$\mu(\mathcal{X}^*)$ is close to $\mu(X)$. We propose a discretization of
distance distribution and in terms of this discretization obtain a lower bound
for $\mu(\mathcal{X}^*)$.
