On the representation of measures over bounded lattices

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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 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
Original languageEnglish
Article number56
JournalAlgebra Universalis
Volume82
Issue number4
DOIs
Publication statusPublished - Nov 2021

Bibliographical note

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

Copyright:
Copyright 2021 Elsevier B.V., All rights reserved.

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