p-convergence in measure of a sequence of measurable functions and corresponding minimal elements of c 0

p-convergence in measure of a sequence of measurable functions and corresponding minimal elements... 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Positivity Springer Journals

p-convergence in measure of a sequence of measurable functions and corresponding minimal elements of c 0

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Publisher
Birkhäuser-Verlag
Copyright
Copyright © 2008 by Birkhäuser Verlag Basel/Switzerland
Subject
Mathematics; Fourier Analysis; Operator Theory; Potential Theory; Calculus of Variations and Optimal Control; Optimization; Econometrics
ISSN
1385-1292
eISSN
1572-9281
D.O.I.
10.1007/s11117-008-2185-z
Publisher site
See Article on Publisher Site

Abstract

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.

Journal

PositivitySpringer Journals

Published: May 27, 2008

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