Let $\lbrace X(t)\mid t\in T \rbrace$ be a stochastic process, where $X(t)$ is a random variable on the probability space $(\Omega,\mathcal{F},{P})$ Writing $X(t)$ as $X(t,\omega)$ where $t\in T$ and $\omega\in\Omega$ we see that if we fix the sample point $\omega$ we have a function in $t$ $X_{\omega}(t) \colon t\mapsto X(t)$ This function $X_{\omega}(t)$ of $t$ is called a sample function, or sample path of the stochastic process.