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Sets with Distinct Sums of Pairs, Long Arithmetic Progressions, and Continuous Mappings

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Abstract

We show that if φ: ℝ → ℝ is a continuous mapping and the set of nonlinearity of φ has nonzero Lebesgue measure, then φ maps bijectively a certain set that contains arbitrarily long arithmetic progressions onto a certain set with distinct sums of pairs.

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Authors and Affiliations

  1. School of Applied Mathematics, National Research University Higher School of Economics, 34, Tallinskaya St., Moscow, 123458, Russia

    V. Lebedev

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  1. V. Lebedev
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Correspondence to V. Lebedev.

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Dedicated to the memory of Jean-Pierre Kahane

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Lebedev, V. Sets with Distinct Sums of Pairs, Long Arithmetic Progressions, and Continuous Mappings. Anal Math 44, 369–380 (2018). https://doi.org/10.1007/s10476-018-0506-4

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  • DOI: https://doi.org/10.1007/s10476-018-0506-4

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