  The following document is a translation (from French to English) of: Gabriele
H. Greco, Sur la mesurabilit\'e d'une fonction num\'erique par rapport \`a une
famille d'ensembles, Rendiconti del Seminario Matematico della Universit\`a di
Padova}, tome 65 (1981), pp. 163--176. Translated by: Jonathan M. Keith, School
of Mathematics, Monash University<EMAIL_ADDRESS>With thanks to:
Prof. Andrea D'Agnolo, Editor-in-Chief of the above journal, for permission to
publish this translation.
