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February 14, 2026Proceedings of the Edinburgh Mathematical Society0 citations

Almost Erdős sets

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ABArian Bërdëllima

Key Points

  • To explore the conditions under which a decreasing null sequence can be classified as an almost Erdős set.
  • Defined almost Erdős sets in terms of Lebesgue measure and linear transformations.
  • Analyzed the behavior of decreasing null sequences with a decay rate greater than 1/2.
  • Established criteria for nonempty subsets of S under Lebesgue measure.
  • Demonstrated that any decreasing null sequence with a decay rate greater than 1/2 qualifies as an almost Erdős set.
  • Provided examples illustrating the set properties that conform to the almost Erdős definition.

Abstract

Abstract A set S R is almost Erdős if, for every 0, there exists a set E R of positive Lebesgue measure such that \x S: ax+b E\ is nonempty for all |a| and b R. In this note, we show that any decreasing null sequence (xₙ) with decay rate greater than 1/2 is an almost Erdős set.

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Cite This Study

Arian Bërdëllima (2026) studied this question.

synapsesocial.com/papers/699011172ccff479cfe57862https://doi.org/10.1017/s0013091526101370
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