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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

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