Laws of large numbers for Cesàro alpha-integrable random variables under dependence condition AANA or AQSI

Both residual Cesàro alpha-integrability (RCI(.)) and strongly residual Cesàro alpha-integrability (SRCI(.)) are two special kinds of extensions to uniform integrability, and both asymptotically almost negative association (AANA) and asymptotically quadrant sub-independence (AQSI) are two special kinds of dependence structures. By relating the RCI(.) property as well as the SRCI(.) property with dependence condition AANA or AQSI, we formulate some tail-integrability conditions under which for appropriate . the RCI(.) property yields L 1-convergence results and the SRCI(.) property yields strong laws of large numbers, which is the continuation of the corresponding literature.