We characterize convergence in measure of a sequence (f n ) n of measurable functions to a measurable function f by elements of c 0, which express the quality of convergence of (f n ) 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 c 0 which characterize the convergence in measure of (f n ) n to f.
Positivity – Springer Journals
Published: May 27, 2008
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