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On expressible sets and p-adic numbers

  • Jaroslav Hančl (a1), Radhakrishnan Nair (a2), Simona Pulcerova (a3) and Jan Šustek (a1)

Continuing earlier studies over the real numbers, we study the expressible set of a sequence A = (an)n≥1 of p-adic numbers, which we define to be the set EpA = {∑n≥1ancn: cn ∈ ℕ}. We show that in certain circumstances we can calculate the Haar measure of EpA exactly. It turns out that our results extend to sequences of matrices with p-adic entries, so this is the setting in which we work.

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2.N. H. Asmar and R. Nair , Certain averages on the a-adic numbers, Proc. Am. Math. Soc. 114(1) (1992), 2128.

3.V. Beresnevich , H. Dickinson and S. Velani , Measure theoretic laws for lim sup sets, Memoirs of the American Mathematical Society, Volume 179 (American Mathematical Society, Providence, RI, 2006).

12.J. Hančl , R. Nair and J. Šustek , On the Lebesgue measure of the expressible set of certain sequences, Indagationes Math. 17(4) (2006), 567581.

13.J. Hančl and J. Šustek , Expressible sets of certain sequences with Hausdorff dimension zero, Monatsh. Math. 152(4) (2007), 315319.

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Proceedings of the Edinburgh Mathematical Society
  • ISSN: 0013-0915
  • EISSN: 1464-3839
  • URL: /core/journals/proceedings-of-the-edinburgh-mathematical-society
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