Is there a standard notation for the measure $E \mapsto \mu(E \cap S)$?

Question

If $\mu$ is a measure and $S$ is $\mu$-measurable, it is easy to see that the measure $E \mapsto \mu(E \cap S)$ defines a measure on the $\sigma$-algebra where $\mu$ is defined. I have been using the notation $\mu_S$ to denote this measure. However, I would like to use a standard notation, if there is one available.