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On the representation of measures over bounded lattices

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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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Authors and Affiliations

  1. Department of Mathematics, CAECE, Buenos Aires, Argentina

    César Massri

  2. IMAS Institute, UBA-CONICET, C1428EGA, Buenos Aires, Argentina

    César Massri

  3. Instituto de Física (IFLP-CCT-CONICET), Universidad Nacional de La Plata, C.C. 727, 1900, La Plata, Argentina

    Federico Holik

  4. Center Leo Apostel for Interdisciplinary Studies and, Department of Mathematics, Brussels Free University, Krijgskundestraat 33, 1160, Brussels, Belgium

    Federico Holik

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  1. César Massri
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  2. Federico Holik
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Correspondence to César Massri.

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Presented by V. Marra.

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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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