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 X such that a measure over X is the same as a (scheme-theoretic) measure over X. We also define the measurability of a lattice, and describe measures over finite lattices
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