On p‐Convergence in Measure of a Sequence of Measurable Functions
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In the study by Papanastassiou and Papachristodoulos, 2009 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 ℳ is a complete but not compact metric space.
QA1-939, measurable functions, p-convergence in measure; convergence in measure; complete metric space., compact metric space, Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence, Mathematics, convergence in measure
QA1-939, measurable functions, p-convergence in measure; convergence in measure; complete metric space., compact metric space, Measurable and nonmeasurable functions, sequences of measurable functions, modes of convergence, Mathematics, convergence in measure
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