Whenever editing is allowed on the nLab again, this article should be ported over there.
In measure theory, a probability measure on a $\sigma$-frame or more generally a $\sigma$-complete distributive lattice is a probability valuation such that the elements are mutually disjoint and the probability valuation is denumerably/countably additive
In measure theory, a probability measure on a $\sigma$-frame or more generally a $\sigma$-complete distributive lattice is a probability valuation with
representing the mutually disjoint elements condition and the denumerably/countably additive condition.