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Local dimension and regular points

Published online by Cambridge University Press:  24 October 2008

Martin T. Barlow  and
S. James Taylor
Martin T. Barlow
Affiliation:
Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB
S. James Taylor
Affiliation:
Department of Mathematics, Maths-Astronomy Building, University of Virginia, Charlottesville, VA 22903, U.S.A.
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Extract

The Hausdorff–Besicovitch dimension of a set A ⊆ ℝd, denoted dim (A), relates to the structure of A in the neighbourhood of its thickest point. If A is irregular then one may wish for an index which will describe the size of A in different places. The obvious definition of the local dimension of A near x is

and it is not hard to verify that

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 112 , Issue 2 , September 1992 , pp. 361 - 368
Copyright
Copyright © Cambridge Philosophical Society 1992

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References

REFERENCES

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