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On the representation of measures over bounded lattices

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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Correspondence to César Massri.

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Massri, C., Holik, F. On the representation of measures over bounded lattices. Algebra Univers. 82, 56 (2021). https://doi.org/10.1007/s00012-021-00741-6

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Keywords

  • Lattices
  • Measurability
  • Measure Functor
  • Representability

Mathematics Subject Classification

  • 06B15
  • 03G10
  • 46E27
  • 28E05
  • 14A25