p-q-convergence of sequences of measurable functions |
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Authors: | C Papachristodoulos W Wilczynski |
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Institution: | a Department of Mathematics, University of Athens, Greece b Department of Mathematics, University of ?ód?, Poland |
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Abstract: | We introduce new types of convergence of sequences of measurable functions stronger than convergence in measure for each pair of positive real numbers p, q and we obtain a classification of convergences in measure. Also in the space M of sequences of measurable functions converging in measure to zero, we introduce in a natural way an equivalence relation ∼, and in the quotient space M=M/∼ a metric, under which M turns to be a complete metric space. |
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Keywords: | primary 28A20 secondary 40A05 |
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