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Extension of a class of decomposable measures using fuzzy pseudometrics. (English) Zbl 1284.28017
Summary: In this paper, we consider a topological approach to extension of t-conorm-based decomposable measures by introducing a fuzzy pseudometric structure on an algebra of sets. We prove that every non-strict continuous Archimedean t-conorm-based decomposable measure can be extended from an algebra to the completion of this algebra under the fuzzy pseudometric and then to the sigma-algebra generated by this algebra. The existence of such an extension follows very simply from the well-known Carathéodory result. However, our topological proof offers an intuitive interpretation of the extension of decomposable measures.

MSC:
28E10 Fuzzy measure theory
54A40 Fuzzy topology
54H05 Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
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