In measure theory, a content on a distributive lattice$(L, \leq, \bot, \vee, \top, \wedge)$ is a valuation$\mu:L \to [0, \infty]$ to the non-negative lower reals such that the valuation of the bottom element is zero and additive if the pair of elements is disjoint.

$\forall a\in L. \forall b \in L. \mu(\bot) = 0$

$\forall a\in L. \forall b \in L. (a \wedge b = \bot) \implies (\mu(a \vee b) = \mu(a) + \mu(b))$