Abstract In this note, the authors 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, the
authors prove that convergence in capacity is stronger than convergence in distribution,
and give some equivalent characterizations of convergence in distribution. In addition,
they give a dominated convergence theorem under sublinear expectations, which may have
its own interest.