The origins of the concept of dimension
R. Duda (1979)
Colloquium Mathematicae
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R. Duda (1979)
Colloquium Mathematicae
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A relationship between the information dimension and the average dimension of a measure is given. Properties of the average dimension are studied.
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For every ε > 0, any subset of ℝⁿ with Hausdorff dimension larger than (1-ε)n must have ultrametric distortion larger than 1/(4ε).
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We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.
Themis Mitsis (2004)
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We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
D. A. Moran (1973)
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