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On the complexity of the ideal of absolute null sets

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Ukrainian Mathematical Journal Aims and scope

Answering a question posed by Banakh and Lyaskovska, we prove that, for an arbitrary countable infinite amenable group G, the ideal of sets having μ-measure zero for every Banach measure μ on G is an Fσδ subset of {0; 1}G.

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References

  1. T. Banakh and N. Lyaskovska, “Completeness of invariant ideals in groups,” Ukr. Mat. Zh., 62, No. 8, 1022–1031 (2010); English translation: Ukr. Math. J., 62, No. 8, 1187–1198 (2010).

  2. J. L. Kelley, “Measures on Boolean algebras,” Pacif. J. Math., 9, 1165–1177 (1959).

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  3. A. Paterson, Amenability, American Mathematical Society (1988).

  4. S. Wagon, The Banach–Tarski Paradox, Cambridge University Press, Cambridge (1986).

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Authors and Affiliations

  1. Institute of Mathematics, University of Warsaw, Warsaw, Poland

    P. Zakrzewski

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  1. P. Zakrzewski
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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 64, No. 2, pp. 275–276, February, 2012.

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Zakrzewski, P. On the complexity of the ideal of absolute null sets. Ukr Math J 64, 306–308 (2012). https://doi.org/10.1007/s11253-012-0647-8

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  • DOI: https://doi.org/10.1007/s11253-012-0647-8

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