  Measure and integral are two closely related, but distinct objects of study.
Nonetheless, they are both real-valued lattice valuations: order preserving
real-valued functions $\phi$ on a lattice $L$ which are modular, i.e.,
$\phi(x)+{\phi}(y) = \phi(x\wedge y)+{\phi}(x\vee y)$ for all $x,y \in L$. We
unify measure and integral by developing a theory for lattice valuations. We
allow these lattice valuations to take their values from the reals, or any
suitable ordered Abelian group.
