On the measurability of a numerical function with respect to a family of sets

The following document is a translation (from French to English) of: Gabriele H. Greco, Sur la mesurabilité d’une fonction numérique par rapport à une famille d’ensembles, Rendiconti del Seminario Matematico della Università di Padova}, tome 65 (1981), pp. 163–176. Translated by: Jonathan M. Keith, School of Mathematics, Monash University, jonathan.keith@monash.edu. With thanks to: Prof. Andrea D’Agnolo, Editor-in-Chief of the above journal, for permission to publish this translation.