Given a decreasing sequence {aⁿ} of nonnegative terms, we prove that there exist subsequences {nk } of {n} such that ∑k=1∞nk+1−nkank and ∑n=1∞an have the same convergence. In particular, ∑n=1∞an ...

In this paper, convergence of series and almost sure convergence are established for weighted random variables under a sub-linear expectation space. Our results are very extensive versions which ...