  In this note, we will survey the existing convergence results for random
variables under sublinear expectations, and prove some new results. Concretely,
under the assumption that the sublinear expectation has the monotone continuity
property, we will prove that $L^p$ convergence is stronger than convergence in
capacity, convergence in capacity is stronger than convergence in distribution,
and give some equivalent characterizations of convergence in distribution. In
addition, we give a dominated convergence theorem under sublinear expectations,
which may have its own interest.
