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Valuations on complemented lattices. (English) Zbl 0843.06005
It is proved that the space of all bounded real-valued valuations \(m\) with \(m(0)= 0\) on a complemented lattice is isomorphic to the space of all real-valued totally additive measures on a suitable complete Boolean algebra. This answers a question of P. Pták affirmatively. The proof is based on a Hahn-decomposition theorem and an extension theorem for valuations.

MSC:
06C15 Complemented lattices, orthocomplemented lattices and posets
28A12 Contents, measures, outer measures, capacities
06E10 Chain conditions, complete algebras
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