Convergence in distribution of random variables question $X, X_1, X_2,\ldots $ are real random variables with $\mathbb{P}(X_n\leq x)\to \mathbb{P}(X\leq x)$ whenever $\mathbb{P}(X=x)=0$.
Why does $X_n\stackrel{L}{\to} X$? At the least, where would I begin?

Start with the definition of what is the convergence. There is also a theorem (http://fr.wikipedia.org/wiki/Convergence_en_loi, can't find the english version) that says that you need to prove that $P(X_n \in A) -> P(X \in A)$ for any A an open
