An orthomodular lattice admitting no group-valued measure
Mirko Navara · Proceedings of the American Mathematical Society · 1994
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.