Editing Convergence of random variables (section)

===Properties===
* Almost sure convergence implies convergence in probability (by [[Fatou's lemma]]), and hence implies convergence in distribution.  It is the notion of convergence used in the strong [[law of large numbers]].
* The concept of almost sure convergence does not come from a [[topology]] on the space of random variables. This means there is no topology on the space of random variables such that the almost surely convergent sequences are exactly the converging sequences with respect to that topology. In particular, there is no metric of almost sure convergence.