The Metrics In Sublinear Expectation Spaces, And Their Properties And Applications

In the classical probability space, V.M.Zolotarev, R.M.Dudely, S.T.Rachev have given the concepts of metrics between real-valued random variables, and studies their properties and applications in detail. But so far, there doesn’t have the metrics’con-cept in the framework of sublinear expectation space, and the corresponding random variable metrics’researches seem to be blank. So in this paper, we will study the same problems in sublinear expectation spaces, Firstly, we introduce the definition of metrics in the framework of sublinear expectation space; Secondly, we explore the properties of metrics, such as the Regular, the (K, r)— homogeneous; Finally, we study the re-lationship between metrics and sequence convergences, including Ky Fan metric convergence and the capacity convergence, and with the condition of random variables sequences’uniformly bounded,we demonstrate the Lp convergence and capacity con-vergence with norm convergence are equivalent, Kantorovich metric convergence and the distribution convergence are equivalent. Additionally, Toepliz Theorem, Cesaro Theorem, Kronecker Theorem are also established.