Abstract

We discuss the infinite measure counterpart of Zolezzi's Theorem for infinite measure spaces. For a measure space with infinite measure, (Ω,Σ,μ)(\Omega, \Sigma, \mu), we construct a sequence in L∞(μ)L^\infty(\mu), with uniformly control upon its support measure, that does not converge in Lp(μ)L^p(\mu), for all 1≤p<∞1\le p < \infty, however does converge weakly in L∞(μ)L^\infty(\mu).

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Keywords

  • Constructive counterexamples
  • Lebesgue spaces

Mathematics Subject Classification

46E30

References

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Suggested citation

K. Teixeira. “On Zolezzi's Theorem for Infinite Measure Spaces.” Journal of Convex Analysis 30 (2023), No. 1, 1–4. https://doi.org/10.68381/jca30001

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Published by Heldermann Verlag, 2023. Rights now held by Banach Press LLC.