Distribution of roots of quasianalytic functions

For functions of certain quasianalytic classes $C\{m_n\}$ on $(-\infty,\infty)$ we determine a function $\xi(x)$, depending on $\{m_n\}$, which is such that a sequence $\{x_k\}$ is a sequence of the roots of $f(x)\in C\{m_n\}$ if and only if for some $a$
$$ \int_a^\infty\frac{dn(x)}{\xi(x - a)}<\infty, $$
where $n(x)$ is a distribution function of the sequence $\{x_k\}$.