Sufficient conditions for uniform continuity of the family of nonadditive weakly regular set functions and their applications (Q2763017)
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scientific article; zbMATH DE number 1689854
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Sufficient conditions for uniform continuity of the family of nonadditive weakly regular set functions and their applications |
scientific article; zbMATH DE number 1689854 |
Statements
22 January 2002
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set functions
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regularity
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uniform continuity
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Sufficient conditions for uniform continuity of the family of nonadditive weakly regular set functions and their applications (English)
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In the paper there are considered scalar nonadditive set functions defined on the algebra of subsets of a \(\sigma\)-topological space being regular with respect to the class of closed sets. These functions may have infinite values. Sufficient conditions are received, due to which the uniform weak continuity of the family of such set functions implies the uniform continuity of their supremations. Some examples of these conditions in particular topological spaces are presented.
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