modification of a stochastic process

Let ${\{X_t\}}_{t\ge 0}$, ${\{Y_t\}}_{t\ge 0}$ be stochastic processes on $(\mathrm{\Omega },ℱ,P)$. ${\{X_t\}}_{t\ge 0}$ is a modification of ${\{Y_t\}}_{t\ge 0}$ if

$$P[\{\omega :X_t(\omega )=Y_t(\omega )\}]=1$$

for all $t\in [0,\mathrm{\infty }).$