摘要
In this paper, by establishing a Borel–Cantelli lemma for a capacity which is not necessarily continuous, and a link between a sequence of independent random variables under the sub-linear expectation and a sequence of independent random variables on R^(∞) under a probability, we give the sufficient and necessary conditions of the strong law of large numbers for independent and identically distributed random variables under the sub-linear expectation, and the sufficient and necessary conditions for the convergence of an infinite series of independent random variables, without the assumption on the continuity of the capacities. A purely probabilistic proof of a weak law of large numbers is also given.
基金
Supported by grants from the NSF of China(Grant Nos.11731012,12031005)
Ten Thousands Talents Plan of Zhejiang Province(Grant No.2018R52042)
NSF of Zhejiang Province(Grant No.LZ21A010002)
the Fundamental Research Funds for the Central Universities。