Journal of Convex Analysis 30 (2023), No. 1, 001--004
Copyright Heldermann Verlag 2023
On Zolezzi's Theorem for Infinite Measure Spaces
Katiuscia Teixeira
Dept. of Mathematics, University of Central Florida, Orlando, U.S.A.
katiuscia.teixeira@ucf.edu
[Abstract-pdf]
We discuss the infinite measure counterpart of Zolezzi's Theorem for infinite measure spaces. For a measure space with infinite measure, $(\Omega, \Sigma, \mu)$, we construct a sequence in $L^\infty(\mu)$, with uniformly control upon its support measure, that does not converge in $L^p(\mu)$, for all $1\le p < \infty$, however does converge weakly in $L^\infty(\mu)$.
Keywords: Constructive counterexamples, Lebesgue spaces.
MSC: 46E30.
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