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In this paper, we obtain a new kind of strong law of large numbers in sublinear expectation spaces without the independent or identically distributed assumption. Instead, the strong law of large numbers is based on some restrictions on the sub-linear expectations of the partial sums. As an application, we give an interesting example in which the random variable sequence enjoys our moment restrictions, but does not enjoy the independent conditions introduced by Marinacci ( 1999 ), Peng ( 2009 ), Chen, Wu, and Li ( 2013 ), Zhang ( 2016b ), nor Chen, Huang, and Wu ( 2019 ).

Strong law of large numbers under moment restrictions in sublinear expectation spaces