Let $(\Omega,\mathcal{F},P)$ be a probability space. Let $(X_{n})_{n\in\mathbb{N}}$ be a sequence of random variables, and $X$ be another RV. $X_n\to X$ in probability if $\forall \epsilon>0:$ $$P(|X_n-X|\ge\epsilon)\to0$$we write it as $$X_{n}\xrightarrow{p}X$$