Pseudo-convergences of sequences of measurable functions on monotone multimeasure spaces (Q2919603)
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scientific article; zbMATH DE number 6090222
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pseudo-convergences of sequences of measurable functions on monotone multimeasure spaces |
scientific article; zbMATH DE number 6090222 |
Statements
4 October 2012
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modes of pseudoconvergence
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Egoroff type theorem
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non-additive multimeasure
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continuity from below and from above
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pseudo-almost everywhere convergence
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pseudo-almost uniform convergence
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pseudo-convergence in measure
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0.97067153
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0.92580664
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0.91423047
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0.9087144
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0.90297407
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Pseudo-convergences of sequences of measurable functions on monotone multimeasure spaces (English)
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Modes of convergence of sequences of real-valued functions defined on a measurable space equiped with some non-additive substitute of multimeasure are defined and compared. A monotone (pseudo-)multimeasure takes closed (bounded, convex) values from some normed linear space. 12 kinds of various pseudo-continuity notions are considered. On the basis of this setting an Egoroff-type theorem is proved for pseudo almost uniform convergence with respect to introduced non-additive multimeasure and then a nonhereditary character of this sort of pseudo-convergence is explained. Multivalued analogues of Lebesgue and Riesz type theorems in the setting of such non-additive multimeasure are left to a planned subsquent paper. A similar subject investigates \textit{T. Watanabe} [Fuzzy Sets Syst. 161, No. 22, 2919--2922 (2010; Zbl 1210.28020)].
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