A Comparison of Two Topologies for LFP(ε)
and the Completeness of LFP(S)
Abstract: First, we make a primary comparison of the -topology and the topology of convergence in probability for . Then, using the relation of the two kinds of topologies for , we give a proof of Stricker’s lemma based on a result in the theory of random normed modules. At last, we show that the random normed module is complete if and only if is complete.
文章引用: 吴明智 , 赵 媛 (2013) LFP(ε) 上两种拓扑的比较与LFP(S) 的完备性。 理论数学， 3， 81-86. doi: 10.12677/PM.2013.31013
 D. Filipović, M. Kupper and N. Vogelpoth. Separation and duality in locally -convex modules. Journal of Functional Analysis, 2009, 256: 3996-4029.
 D. Filipović, M. Kupper and N. Vogelpoth. Approaches to conditional risks. Working Paper Series No. 28, Vienna: Vienna Institute of Finance, 2009.
 T. X. Guo. Recent progress in random metric theory and its applications to conditional risk measures. Science China Mathematics, 2011, 54(4): 633-660.
 T. X. Guo. Relations between some basic results derived from two kinds of topologies for a random locally convex module. Journal of Functional Analysis, 2010, 258: 3024-3047.
 T. X. Guo, S. B. Li. The James theorem in complete random normed modules. Journal of Mathematical Analysis and Applications, 2005, 308: 257-265.
 M. Z. Wu. The Bishop-Phelps theorem in complete random normed modules endowed with the -topology. Journal of Mathematical Analysis and Applications, 2012, 391: 648-652.
 严加安. 测度论讲义[M]. 北京: 科学出版社, 2004.
 B. Schweizer, A. Sklar. Probabilistic metric spaces. New York: Dover Publications, 2005.
 H. Fӧllmer, A. Schied. Stochastic finance, an introduction in discrete time. Berlin, New York: Walter de Gruyter, 2002.
 T. X. Guo, G. Shi. The algebraic structure of finitely generated -modules and the Helly theorem in random normed modules. Journal of Mathematical Analysis and Applications, 2011, 381: 833-842.