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Rings of fractional dimension

Part of: Classical measure theory

Published online by Cambridge University Press:  26 February 2010

K. J. Falconer
K. J. Falconer
Affiliation:
School of Mathematics, University Walk, Bristol. BS8 1TW
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Extract

We define s-dimensional Hausdorff outer measure on subsets of ℝn by

Here | | denotes the diameter of a set. The Souslin sets, which include the Borel sets, are Hs-measurable for any s ≥ 0.

MSC classification

Secondary: 28A75: Length, area, volume, other geometric measure theory
Type
Research Article
Information
Mathematika , Volume 31 , Issue 1 , June 1984 , pp. 25 - 27
Copyright
Copyright © University College London 1984

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References

1.Davies, Roy O.. Subsets of finite measure in analytic sets, Indag. Math., 14 (1952), 488–489.CrossRefGoogle Scholar
2.Davies, Roy O.. Two counter-examples concerning Hausdorff dimension of projections. Coiloq. Math., 42 (1979), 53–58.CrossRefGoogle Scholar
3.Erdős, P.. Some remarks on subgroups of real numbers. Coiloq. Math., 42 (1979), 119–120.CrossRefGoogle Scholar
4.Erdős, P. and Volkmann, B.. Additive Gruppen mit vorgegebener Hausdorffscher Dimension. J. Reine Angew. Math., 221 (1966), 203–208.Google Scholar
5.Falconer, K. J.. Hausdorff dimension and the exceptional set of projections. Mathematika, 29 (1982), 109–115.CrossRefGoogle Scholar
6.Falconer, K. J.. The geometry of fractal sets (Cambridge University Press, 1984).Google Scholar
7.Kahnert, D.. Hausdorff-Masse von Summennengen I. J. Reine Angew. Math., 264 (1973), 1–28.Google Scholar
8.Kahnert, D.. Hausdorff-Masse von Summennengen II. J. Reine Angew. Math., 266 (1974), 1–9.Google Scholar
9.Marstrand, J. M.. The dimension of Cartesian product sets. Proc. Cambridge Phil. Soc., 50 (1954), 198–202.CrossRefGoogle Scholar
10.Volkmann, B.. Eine metrische Figenschaft reeller Zahlkörper. Math. Annalen, 141 (1960), 237–238.CrossRefGoogle Scholar