Measure of Set Difference with Subset

Theorem
Let $\struct {X, \Sigma, \mu}$ be a measure space.

Let $S, T \in \Sigma$ be such that $S \subseteq T$, and suppose that $\mu \paren S < +\infty$.

Then:


 * $\mu \paren {T \setminus S} = \mu \paren T - \mu \paren S$

where $T \setminus S$ denotes set difference.