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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.


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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