Marcinkiewicz's strong law of large numbers for nonlinear expectations

The sub-linear expectation space is a nonlinear expectation space having advantages of modeling the uncertainty of probability and distribution. In the sub-linear expectation space, we use capacity and sub-linear expectation to replace probability and expectation of classical probability theory. In this paper, the method of selecting subsequence is used to prove Marcinkiewicz's strong law of large numbers under sub-linear expectation space. This result is a natural extension of the classical Marcinkiewicz's strong law of large numbers to the case where the expectation is nonlinear. In addition, this paper also gives a theorem about convergence of a random series.