convergence in distribution

Definition

Suppose sequence $X_1, X_2,...$ has cdf $F_n(x)$, and random variable $X$ has cdf $F(x)$. The sequence is said to converge in distribution (d) to $X$, i.e. $X_n \ \xrightarrow{d}\ X$, if

for all $x$ at which $F(x)$ is continuous.

References

1. https://www.probabilitycourse.com/chapter7/7_2_4_convergence_in_distribution.php