2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/157079We describe a new framework of a sublinear expectation space and the related notions and results of distributions, independence. A new notion of G-distributions is introduced which generalizes our G-normal-distribution in the sense that mean-uncertainty can be also described. W present our new result of central limit theorem under sublinear expectation. This theorem can be also regarded as a generalization of the law of large number in the case of mean-uncertainty.ProbabilityStatistics Theory60H10, 60H05, 60H30text