Limiting behaviors for weighted sums of residually $h$-integrable random variables under sublinear expectations

This paper investigates the weak law of large numbers, complete convergence for weighted sums of residually $h$-integrable extended negatively dependent random variables (r.v.'s), and complete integral convergence for weighted sums of strongly residually $h$-integrable extended negatively dependent r.v.'s under sublinear expectations. The results obtained in the paper markedly improve and extend some existing ones in the probability space and sublinear expectation space.