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The Hausdorff Dimension Distribution of Finite Measures in Euclidean Space

Published online by Cambridge University Press:  20 November 2018

Colleen D. Cutler
Colleen D. Cutler*
Affiliation:
University of Waterloo, Waterloo, Ontario
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Let E be a Borel set of RN. The α-outer Hausdorff measure of E has been defined to be

where

and each Bi is a closed ball. d(Bi) denotes the diameter of Bi.

It is easily seen that the same value Hα(E) is obtained if we consider coverings of E by open balls or by balls which may be either open or closed.

By dim(E) we will mean the usual Hausdorff-Besicovitch dimension of E, where

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 38 , Issue 6 , 01 December 1986 , pp. 1459 - 1484
Copyright
Copyright © Canadian Mathematical Society 1986

References

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