An orthomodular lattice admitting no group-valued measure

Navara, Mirko

doi:10.1090/S0002-9939-1994-1191871-X

An orthomodular lattice admitting no group-valued measure
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Proc. Amer. Math. Soc. 122 (1994), 7-12 Request permission

Abstract:

We construct a finite orthomodular lattice L such that, for each commutative group G, there is no nontrivial G-valued measure on L. This result extends a result of R. J. Greechie (Orthogonal lattices admitting no states, J. Combin. Theory Ser. A 10 (1971), 119-132), and also sheds light on recent investigations in the noncommutative measure theory.

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