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arXiv · 1805.02254

Sets with distinct sums of pairs, long arithmetic progressions, and continuous mappings

Vladimir Lebedev
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Abstract

We show that if $φ\colon \mathbb R\rightarrow\mathbb R$ 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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Vladimir Lebedev. 2018-09-18. Sets with distinct sums of pairs, long arithmetic progressions, and continuous mappings. https://doi.org/10.1007/s10476-018-0506-4

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