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1
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Typical multifractal box dimensions of measures

100%
Olsen L.
Fundamenta Mathematicae
|
2011
|
tom 211
|
nr 3
245-266
EN
We study the typical behaviour (in the sense of Baire's category) of the multifractal box dimensions of measures on $ℝ^{d}$. We prove that in many cases a typical measure μ is as irregular as possible, i.e. the lower multifractal box dimensions of μ attain the smallest possible value and the upper multifractal box dimensions of μ attain the largest possible value.
2
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Discrete self-similar multifractals with examples from algebraic number theory

100%
Olsen L.
Acta Arithmetica
|
2006
|
tom 123
|
nr 3
233-252
3
Content available remote

Distribution of digits in integers: fractal dimensions and zeta functions

100%
Olsen L.
Acta Arithmetica
|
2002
|
tom 105
|
nr 3
253-277
4
Content available remote

Characterization of local dimension functions of subsets of $ℝ^{d}$

100%
Olsen L.
Colloquium Mathematicum
|
2005
|
tom 103
|
nr 2
231-239
EN
For a subset $E ⊆ ℝ^{d}$ and $x ∈ ℝ^{d}$, the local Hausdorff dimension function of E at x is defined by $dim_{H,loc}(x,E) = lim_{r↘ 0} dim_{H}(E ∩ B(x,r))$ where $dim_{H}$ denotes the Hausdorff dimension. We give a complete characterization of the set of functions that are local Hausdorff dimension functions. In fact, we prove a significantly more general result, namely, we give a complete characterization of those functions that are local dimension functions of an arbitrary regular dimension index.
5
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Extremely non-normal continued fractions

88%
Olsen L.
Acta Arithmetica
|
2003
|
tom 108
|
nr 2
191-202
6
Content available remote

Iterated Cesàro averages, frequencies of digits, and Baire category

45%
Hyde J., Laschos V., Olsen L., Petrykiewicz I., Shaw A.
Acta Arithmetica
|
2010
|
tom 144
|
nr 3
287-293
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