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On the measurable chromatic number of a space of dimension n ≤ 24

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Abstract

This paper is devoted to the classical problem of finding the measurable chromatic number of n-dimensional Euclidean space, i.e., the value χ m (ℝn) equal to the least possible number of Lebesgue measurable sets that do not contain pairs of points at a distance of 1 and cover the whole space. Assuming that a certain hypothesis is true, we significantly improve the lower bounds for χ m (ℝn).

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Authors and Affiliations

  1. Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119992, Russia

    L. I. Bogolubsky & A. M. Raigorodskii

  2. Moscow Institute of Physics and Technology (State Technical University), Institutskii per. 9, Dolgoprudnyi, Moscow oblast, 141700, Russia

    A. M. Raigorodskii

  3. Institute of Mathematics and Informatics, Buryat State University, ul. Ranzhurova 5a, Ulan-Ude, 670000, Buryat Republic, Russia

    A. M. Raigorodskii

Authors
  1. L. I. Bogolubsky
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  2. A. M. Raigorodskii
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Corresponding author

Correspondence to L. I. Bogolubsky.

Additional information

Original Russian Text © L.I. Bogolubsky, A.M. Raigorodskii, 2015, published in Doklady Akademii Nauk, 2015, Vol. 465, No. 6, pp. 647–650.

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Bogolubsky, L.I., Raigorodskii, A.M. On the measurable chromatic number of a space of dimension n ≤ 24. Dokl. Math. 92, 761–763 (2015). https://doi.org/10.1134/S1064562415060344

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  • DOI: https://doi.org/10.1134/S1064562415060344

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