Restricted Measure is Measure

Theorem
Let $\left({X, \mathcal A, \mu}\right)$ be a measure space.

Let $\mathcal B$ be a sub-$\sigma$-algebra of $\mathcal A$.

Then the restricted measure $\mu \restriction_{\mathcal B}$ is a measure on the measurable space $\left({X, \mathcal B}\right)$.