Law

Last updated Nov 1, 2022

Let $(\Omega, \mathcal{A}, \mathbb{P})$ be a Probability Space, let $(T, \leq)$ be a Total Ordering, and let $(S, \Sigma)$ be a Measure Space. Let $X: \Omega \to S^{T}$ be a Stochastic Process. Then the Law of $X$ is its Induced Probability Measure on $S^{T}$:

$$\mu := \mathbb{P} \circ X^{-1}$$