Valuations on complemented lattices (Q1907596)
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scientific article; zbMATH DE number 844098
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Valuations on complemented lattices |
scientific article; zbMATH DE number 844098 |
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Valuations on complemented lattices (English)
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15 August 1996
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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.
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bounded real-valued valuations
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complemented lattice
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real-valued totally additive measures
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complete Boolean algebra
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