On the essential union and intersection of families
of measurable sets

Abstract. In this short note, we demonstrate that in a \(\sigma\)-finite measure space the union and the intersection of arbitrary (i.e., not necessary countable) families of measurable sets can be defined in a natural manner. By examples, we also show that the \(\sigma\)-finiteness of the underlying measure space is only sufficient for this property but not necessary.

Key words and phrases. Essential union and intersection of measurable sets.