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Representation and extension of states on MV-algebras. (English) Zbl 1101.06008

The paper deals with the representation of finitely additive states on Archimedean MV-algebras, which are isomorphic with the clan of continuous fuzzy functions on a compact Hausdorff topological space via integrals. In addition, it is shown that every finitely additive measure on a Boolean subalgebra of an MV-algebra can be extended to a finite state (not necessarily unique) on the whole MV-algebra.

MSC:

06D35 MV-algebras
28E99 Miscellaneous topics in measure theory
54A40 Fuzzy topology
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