Toeplitz Lemma, Cesaro Mean Convergence Theorem And Kronecker Lemma Under Sublinear Expectations

In this thesis, we study the Toeplitz lemma, the Cesaro mean convergence theorem and the Kronecker lemma under sublinear expectations. At first, we consider "quasi-surely convergence", "mean convergence" and "convergence in capacity" versions of the Toeplitz lemma, the Cesaro mean convergence theorem and the Kronecker lemma under sublinear expectations. Secondly, we define the complete convergence and two classes of complete moment convergence. Finally, we consider the Toeplitz lemma, the Cesaro mean convergence theorem and the Kronecker lemma under complete convergence and these two classes of complete moment convergence, and give some sufficient conditions for the Cesaro mean convergence theorem under the new three classes of convergences.