On the existence of a minimal generating set for $σ$-algebras

Abstract

Does there exist for any $σ$-algebra a minimal (with respect to inclusion) generating set? We formulate this problem and answer it in the very special instance of partition generated and standard measurable spaces, the general case remaining open.

Problem already previously solved; http://matwbn.icm.edu.pl/ksiazki/fm/fm124/fm12417.pdf