Sigma-Algebra is Delta-Algebra

Theorem
A $\sigma$-algebra is also a $\delta$-algebra.

Proof
Let $\mathcal S$ be a $\sigma$-algebra whose unit is $\mathbb U$.

Let $A_1, A_2, \ldots$ be a countably infinite collection of elements of $\mathcal S$.

Then:

Thus $\mathcal S$ is a $\delta$-algebra.

Also see

 * Delta-Algebra is Sigma-Algebra