关于随机最远点(英文)

On Random Farthest Points

首先给出在随机赋范模中子集的随机最远点的概念.进一步,利用随机一致凸性和经典一致凸性之间的联系证明了下面的结果:令(E,||·||)为完备的随机一致凸的随机赋范模,S为E中几乎处处有界并在(ε,λ)-拓扑下的闭子集,则具有S中随机最远点的集合稠于E.

In this paper, we first present the notion of random farthest points of subsets in random normed modules. Then, we make use of the relation between random uniform convexity and classical uniform convexity to prove the following result： let （E, ｜｜·｜｜） be a complete random uniformly convex random normed module and S an almost surely bounded and closed subset of E under the （ε, λ）-topology, then the set of all points which have a random farthest point in S is dense in E.