The authors investigate measures of pseudorandomness of finite sequences \((x_n)\) of real numbers. They extend the well-distribution measure introduced by \textit{C. Mauduit} and \textit{A. Sárközy} [Acta Arith. 82, No. 4, 365--377 (1997; Zbl 0886.11048)], which analyzes the behavior of a sequence \((x_n)\) along arithmetic progressions \((x_{ak+b})\), by replacing the class of arithmetic progressions by an arbitrary class \({\mathcal A}\) of sequences of positive integers. They show that this generalized measure is closely related to the metric entropy of the class \({\mathcal A}\). This fact is used to derive precise bounds for the pseudorandomness measure of classical constructions, in particular, `truly' random sequences and sequences of the form \(\{n_k\omega\}\), where \(\{.\}\) denotes the fractional part, \(\omega\in [0,1)\) and \((n_k)\) is a given sequence of integers.