Compactivorous sets in Banach spaces
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- by Davide Ravasini PDF
- Proc. Amer. Math. Soc. 150 (2022), 2121-2129
Abstract:
A set $E$ in a Banach space $X$ is compactivorous if for every compact set $K$ in $X$ there is a nonempty, (relatively) open subset of $K$ which can be translated into $E$. In a separable Banach space, this is a sufficient condition which guarantees the Haar nonnegligibility of Borel subsets. We give some characterisations of this property in both separable and nonseparable Banach spaces and prove an extension of the main theorem to countable products of locally compact Polish groups.References
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Additional Information
- Davide Ravasini
- Affiliation: Institut für Mathematik, Universität Innsbruck, Technikerstraße 13, 6020 Innsbruck, Austria
- ORCID: 0000-0001-6355-5802
- Email: davide.ravasini@uibk.ac.at
- Received by editor(s): May 17, 2021
- Received by editor(s) in revised form: August 28, 2021, and August 30, 2021
- Published electronically: February 7, 2022
- Additional Notes: The work of the author was supported by the Austrian Science Fund (FWF): P 32523-N
- Communicated by: Stephen Dilworth
- © Copyright 2022 by the author
- Journal: Proc. Amer. Math. Soc. 150 (2022), 2121-2129
- MSC (2020): Primary 46B20; Secondary 46B50, 54H11
- DOI: https://doi.org/10.1090/proc/15851
- MathSciNet review: 4392346