The Algebraic Structure of Finitely Generated L0(F,K)-modules and the Helly Theorem in Random Normed Modules
Journal of mathematical analysis and applications(2011)
Abstract
Let K be the scalar field of real numbers or complex numbers and L0(F,K) the algebra of equivalence classes of K-valued random variables defined on a probability space (Ω,F,P). In this paper, we first characterize the algebraic structure of finitely generated L0(F,K)-modules and then combining the recently developed separation theorem in random locally convex modules we prove the Helly theorem in random normed modules with the countable concatenation property under the framework of random conjugate spaces at the same time a simple counterexample shows that it is necessary to require the countable concatenation property.
MoreTranslated text
Key words
Finitely generated L0(F,K)-module,Random normed module,Helly theorem
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined