Mathematical Logic Quarterly 54 (5):483-491 (2008)

Abstract
This paper initiates the study of sets in Euclidean spaces ℝn that are defined in terms of the dimensions of their elements. Specifically, given an interval I ⊆ [0, n ], we are interested in the connectivity properties of the set DIMI, consisting of all points in ℝn whose dimensions lie in I, and of its dual DIMIstr, consisting of all points whose strong dimensions lie in I. If I is [0, 1) or
Keywords Kolmogorov complexity  dimension level sets  computable analysis  constructive dimension
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DOI 10.1002/malq.200710060
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References found in this work BETA

Von Mises' Definition of Random Sequences Reconsidered.Michiel van Lambalgen - 1987 - Journal of Symbolic Logic 52 (3):725-755.

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Completeness, Compactness, Effective Dimensions.Stephen Binns - 2013 - Mathematical Logic Quarterly 59 (3):206-218.

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