向量值B类GWT的收敛性

ON CONVERGENCE OF VECTOR-VALUED GWT OF CLASS B

摘要: 本文证明了:若Bonach格E同构于l¹（Γ）的一个子格对某一指标集Γ,则每一个B^-类E值GWT在E中强拓扑下依概率收敛,若E有RNP,则每一个B^-类E^-值GWT在E中强拓扑下依概率收敛。

Abstract: Let （\Omega, \mathscrF, P） be a probability space, and E a Banach lattice.In this paper we prove that （1） if E is isomorphic to a sublatticc ofl¹（Γ） for a certain Г, then every E-valued GWT of class B^- is strongly convergent in pr.and every E-valued subpramart of class B⁺ is strongly convergent a.e.（2） If E have RNP, then every E^--valued GWT of class B^- is strongly convergent in pr.