Proposition (Same Finite-Dimensional Distribution)

Let $X=(X_{t})_{t\ge 0},Y=(Y_{t})_{t\ge 0}$ be processes on $(\Omega,\mathcal{F},P)$.$X,Y$ have the same finite dimensional distribution if $\forall 0\le t_{1}<t_{2}<\dots<t_{N}, \ \forall n\in\mathbb{N}^{*}$, $\forall B_{1},B_{2},\dots,B_{N}\in\mathcal{B}(\mathbb{R})$ we have that $$P(X_{t_{1}}\in B_{1},\dots,X_{t_{N}}\in B_{N})=P(Y_{t_{1}}\in B_{1},\dots,Y_{t_{N}}\in B_{N})$$