Given a probability space $(S,\mathcal{F},\mu)$ and a random variable or random element $f \colon S \to X$, the **law** or **distribution** of $f$ (or sometimes, of $X$) is the probability measure on $X$ which to a measurable subset $A\subseteq X$ assigns the probability that $f$ takes values in $A$.

In particular, the law of $f$ is the pushforward of $\mu$ along $f$.

The law of a deterministic random variable is a Dirac measure.

category: probability

Last revised on February 20, 2024 at 17:43:27. See the history of this page for a list of all contributions to it.