On \(p\)-convergence in measure of a sequence of measurable functions (Q554915)
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scientific article; zbMATH DE number 5930760
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On \(p\)-convergence in measure of a sequence of measurable functions |
scientific article; zbMATH DE number 5930760 |
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On \(p\)-convergence in measure of a sequence of measurable functions (English)
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22 July 2011
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Summary: In a study by \textit{N. Papanastassiou} and \textit{Ch. Papachristodoulos} [Positivity 13, No.~1, 243--253 (2009; Zbl 1189.28001)] the notion of \(p\)-convergence in measure was introduced. In a natural way \(p\)-convergence in measure induces an equivalence relation on the space \(M\) of all sequences of measurable functions converging in measure to zero. We show that the quotient space \(\mathcal M\) is a complete but not compact metric space.
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convergence in measure
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measurable functions
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compact metric space
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