# Syntax for the convergence of random variables

Can anyone explain the syntax from the following Wikipedia article on the convergence of random variables?

In particular:

1. What is the squiggly line?
2. What are $d$, $D$, $L$, $L_X$?
3. Why does it say $X_n$ implies X? They don't seem to be statements
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From the article: "Convergence in distribution may be denoted as [all this variants]". What is your question? –  Grigory M Aug 7 '10 at 10:31
@Grigory M: Updated the question –  Casebash Aug 7 '10 at 10:52
All these symbols are just variants of notation for convergence in distribution. You don't ask "what are these c, o and s you need to multiply to get $\cos$", right? –  Grigory M Aug 7 '10 at 11:19
@Grigory: I really do need to read more carefully –  Casebash Aug 7 '10 at 12:19

All of these expressions are just notations for "X_n converges to $X$ in distribution".
2. The symbols $d$ and $\mathcal D$ stand for distribution, $\mathcal L$ and $\mathcal L_X$ stand for law. (One also speaks of "convergence in law" instead of "convergence in distribution".