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