On the representation of measures over bounded lattices

Federico Holik

doi:10.1007/s00012-021-00741-6

On the representation of measures over bounded lattices

Federico 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 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 language	English
Article number	56
Journal	Algebra Universalis
Volume	82
Issue number	4
DOIs	https://doi.org/10.1007/s00012-021-00741-6
Publication status	Published - Nov 2021

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

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

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On the representation of measures over bounded lattices

Abstract

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