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arXiv · 1705.11051

On the representation of measures over bounded lattices

C. Massri·F. Holik
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Abstract

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.

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C. Massri, F. Holik. 2021-09-17. On the representation of measures over bounded lattices. https://arxiv.org/abs/1705.11051

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