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khinchin–lutz theorem

Proceedings of the Edinburgh Mathematical Society (1)

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On expressible sets and p-adic numbers
Part of
- Probabilistic theory: distribution modulo $1$; metric theory of algorithms
Jaroslav Hančl, Radhakrishnan Nair, Simona Pulcerova, Jan Šustek
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 54 / Issue 2 / June 2011

Published online by Cambridge University Press:

25 February 2011, pp. 411-422
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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.