In measure theory, a $\sigma$-continuous probability valuation on a $\sigma$-complete lattice$(L, \leq, \bot, \vee, \top, \wedge, \Vee)$ is a probability valuation$\mu:L \to [0, 1]$ such that the $\sigma$-continuity condition is satisfied: for all sequences $s:\mathbb{N} \to L$, if $s(n) \leq s(n + 1)$ for all natural numbers $n \in\mathbb{N}$, then