I am studying Turan's proof of the fact that "almost all" $n$ have "very close to" $\ln \ln n$ prime factors. The statement of the theorem is:
Let $\omega (n) \rightarrow \infty$ arbitrarily slowly. Then the number of $x$ in $\{1, 2, ..., n \}$ such that $$|\nu(x)-\ln\ln n|>\omega(n)\sqrt{\ln\ln n}$$ is $o(n)$. Here $\nu(x)$ is the number of distinct prime factors of $x$.
What does the first line (in bold) mean?