  In this paper we investigate measures over bounded lattices, extending and
giving a unifying treatment to previous works. In particular, we prove that the
measures of an arbitrary bounded lattice can be represented as measures over a
suitably chosen Boolean lattice. Using techniques from algebraic geometry, we
also prove that given a bounded lattice $X$ there exists a scheme $\mathcal{X}$
such that a measure over $X$ is the same as a (scheme-theoretic) measure over
$\mathcal{X}$. We also define the measurability of a lattice, and describe
measures over finite lattices.
