I asked this question on StackExchange a few days ago but didn't get any response, so I thought I would try here.

The Wikipedia article on [convergence of measures](http://en.wikipedia.org/wiki/Convergence_of_measures) defines three kinds of convergence: total variation, strong, and weak. For weak convergence, a number of equivalent formulations, but not for strong or total variation convergence. I have two questions.

1. Are there some equivalent formulations for those notions of convergence too? In particular, is it true that $\mu_n$ strongly converges to $\mu$ iff $E_{\mu_n} f\to E_\mu f$ for ever bounded measurable function $f$? According to an answer to [this question](http://math.stackexchange.com/questions/308249/convergence-of-probability-measures-in-total-variation-and-limits-of-integrals), the left-to-right direction holds if strong convergence is strengthened by total variation convergence.

2. Are there some nice characterizations of these topologies that are not stated in terms of convergent sequences?