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p–q-convergence of sequences of measurable functions

Authors
Journal
Topology and its Applications
0166-8641
Publisher
Elsevier
Publication Date
Volume
158
Issue
12
Identifiers
DOI: 10.1016/j.topol.2011.05.020
Keywords
  • Q-Complete Convergence
  • P–Q-Complete Convergence

Abstract

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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