  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. In our previous work we showed that under some
parametric restrictions for distance distribution measure of maximal cluster
structure $\mu(\mathcal{X})^*$ is close $\mu(X)$ and lower bound for
$\mu(\mathcal{X})^*$ converges to $\mu(X)$ when corresponding parameters tend
to 0. However, this bound asymptotically unimprovable. We propose an additional
restriction for distance distribution that is responsible for balance of
cluster's measure in cluster structure. This restriction allows to
significantly improve previous bound in asymptotic sense.

Discrete Mathematics