Let $(X,\mathscr{M},\mu)$ be a measure space, and let $f:X\to \mathbb{R}$ be a $\mathscr{M}$-measurable function. Let $\mathscr{N}$ be the σ-algebra containing all Borel subsets of $\mathbb{R}$. Now define $\mu_{f}:\mathscr{N}\to[0,+\infty]$ as $$\mu_{f}(E):=\mu(f^{-1}(E))\quad E\in\mathscr{N}$$Then $\mu_{f}$ is a measure and it is called the law of $f$.