  Let $\mu$ be a measure from Szeg\H{o} class on the unit circle $\mathbb T$
and let $\{f_n\}$ be the family of Schur functions generated by $\mu$. In this
paper, we prove a version of the classical Szeg\H{o}'s formula which controls
the oscillation of $f_n$ on $\mathbb T$ for all $n \ge 0$. Then, we focus on an
analog of Lusin's conjecture for polynomials $\{\varphi_n\}$ orthogonal with
respect to measure $\mu$ and prove that pointwise convergence of
$\{|\varphi_n|\}$ almost everywhere on $\mathbb T$ is equivalent to a certain
condition on zeroes of $\varphi_n$.
