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Besicovitch pseudodistances with respect to non-Følner sequences

Abstract : The Besicovitch pseudodistance defined in [BFK99] for one-dimensional configurations is invariant by translations. We generalize the definition to arbitrary groups and study how properties of the pseudodistance, including invariance by translations, are determined by those of the sequence of finite sets used to define it. In particular, we recover that if the Besicovitch pseudodistance comes from a nondecreasing exhaustive Følner sequence, then every shift is an isometry. For non-Følner sequences, we prove that some shifts are not isometries, and the Besicovitch pseudodistance with respect to some subsequence even makes them non-continuous.
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https://hal.archives-ouvertes.fr/hal-02566187
Contributor : Pierre Guillon Connect in order to contact the contributor
Submitted on : Wednesday, May 6, 2020 - 8:32:23 PM
Last modification on : Wednesday, November 3, 2021 - 7:31:45 AM

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  • HAL Id : hal-02566187, version 1

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Silvio Capobianco, Pierre Guillon, Camille Noûs. Besicovitch pseudodistances with respect to non-Følner sequences. 2020. ⟨hal-02566187⟩

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