If is a -algebra over and contains an interval, then also contains all open boxes in .

Let and be any -algebras over the same non-empty set . Then the intersection is always a -algebra over .

Let be a set, then is a -algebra over if and only if is neither empty nor uncountable.

If is infinite, then any -algebra over must contain infinitely many sets

If is a finite set, then any -algebra over also contains only finitely many elements.

Let be an arbitrary -algebra over a non-empty set and be an arbitrary subset. Then the generated -algebra .