The fundamental theorem of affine geometry in regular L-0-modules
发布时间：2024-10-25
点击次数：
影响因子：1.3
DOI码：10.1016/j.jmaa.2021.125827
发表刊物：J. Math. Anal. Appl.
关键字：Regular L-0-modules L-0-affine mappings Stable mappings The fundamental theorem of affine geometry
摘要：Let (Omega, F, P) be a probability space and L-0(F) the algebra of equivalence classes of real-valued random variables defined on (Omega, F, P). A left module M over the algebra L-0(F) (briefly, an L-0(F)-module) is said to be regular if x = y for any given two elements x and y in M such that there exists a countable partition {A(n), n is an element of N} of Omega to F such that (I) over tilde (An) . x = (I) over tilde (An ). y for each n is an element of N, where I-An is the characteristic function of A(n) and (I) over tilde (An) its equivalence class. The purpose of this paper is to establish the fundamental theorem of affine geometry in regular L-0 (F)-modules: let V and V' be two regular L-0(F)-modules such that V contains a free L-0(F)-submodule of rank 2, if T : V -> V' is stable and invertible and maps each L-0 -line segment to an L-0-line segment, then T must be L-0-affine.
合写作者：Long Long
第一作者：Mingzhi Wu
论文类型：期刊论文
通讯作者：Tiexin Guo
论文编号：125827
学科门类：理学
一级学科：数学
文献类型：J
卷号：507
ISSN号：0022-247X
是否译文：否
发表时间：2021-11-15
收录刊物：SCI
发布期刊链接：https://www.sciencedirect.com/science/article/pii/S0022247X21009069