What is cid?

$X_n$ converges in distribution (or in law) to $X$, written $X_n \Rightarrow X$, if

Equivalently (Exercise 23.4): $F_{X_n}(t) \to F_X(t)$ at every continuity point $t$ of $F_X$. The $X_n$ need not live on a common probability space: only laws matter.