Definition (Tight)

A sequence of Probability Measures $\{ \mu_{n} \}_{n}$ on $(\mathbb{X},\mathcal{B})$ is said to be tight such that $$\forall\epsilon>0,\exists \text{ compact }K_{\epsilon}\subset \mathbb{X}:\mu_{n}(K_{\epsilon}) > 1 — \epsilon,\forall n\ge 1$$