p-convergence in measure of a sequence of measurable functions and corresponding minimal elements of c
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Authors: | Nikolaos Papanastassiou Christos Papachristodoulos |
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Institution: | (1) Department of Mathematics, University of Athens, Panepistimiopolis, 15785 Athens, Greece |
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Abstract: | We characterize convergence in measure of a sequence (fn)n of measurable functions to a measurable function f by elements of c0, which express the quality of convergence of (fn)n to f. This characterization motivates the introduction of a new notion of convergence, called “p-convergence in measure” (p > 0), which is stronger than convergence in measure. We prove the existence of “minimal” elements in c0 which characterize the convergence in measure of (fn)n to f.
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 28A20 |
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