An $L^0(\mathcal{F},R)-$valued function's intermediate value theorem and its applications to random uniform convexity

Guo TieXin, Zeng XiaoLin

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