Delta-Algebra is Sigma-Algebra

Theorem
Every $\delta$-algebra is a $\sigma$-algebra.

Proof
Let $\DD$ be a $\delta$-algebra whose unit is $\mathbb U$.

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

Then:

Thus $\DD$ is also a $\sigma$-algebra.

Also see

 * Sigma-Algebra is Delta-Algebra