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Let {x n } n∈ℕ be a sequence in [0, 1] d , {λ n }n∈ℕ a sequence of positive real numbers converging to 0, and δ > 1. The classical ubiquity results are concerned with the computation of the Hausdorff dimension of limsup-sets of the form $$ S{\left( \delta \right)} = {\bigcap\limits_{N \in \mathbb{N}} \; {{\bigcup\limits_{n \geqslant N} {B{\left( {x_{n} ,\lambda ^{\delta }_{n} } \right)}} }} }. $$
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Jan 1, 2007
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