Extension of measures on pseudo-D-lattices (Q2822866)
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scientific article; zbMATH DE number 6632923
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Extension of measures on pseudo-D-lattices |
scientific article; zbMATH DE number 6632923 |
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Extension of measures on pseudo-D-lattices (English)
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5 October 2016
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modular measures
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pseudo-D-lattice
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Carathéodory extension
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The authors prove an extension theorem for modular measures defined on pseudo-D-lattices, the noncommutative version of D-lattices. The result is proved constructing an ``outer measure'' like in the Carathéodory theorem which says that every group-valued \(\sigma \)-additive measure defined on a Boolean algebra extends uniquely to the generated \(\sigma \)-algebra. Their result also generalizes a result proved by the reviewer [Fuzzy Sets Syst. 244, 123--129 (2014; Zbl 1315.28008)].
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