The fundamental theorem of affine geometry in regular $L^0$-modules

Mingzhi Wu, Tiexin Guo, Long Long

Let $(\Omega ,\mathcal{F},P)$ be a probability space and $L^0(\mathcal{F})$ the algebra of equivalence classes of real-valued random variables defined on $(\Omega ,\mathcal{F},P)$. A left m…