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A counter-example in area theory

Published online by Cambridge University Press:  24 October 2008

D. J. Ward  and
E. R. Reifenberg
D. J. Ward
Affiliation:
University of Bristol
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In area theory, Hausdorff measure has been mainly used in the form of Hausdorff ‘spherical’ measure (l) in spite of the fact that work on the geometry of sets of points has mainly used Hausdorff ‘convex’ measure (2,4). The reason for this lies in the inequality This inequality is known (1,3) when the measures are interpreted aslspherical’. But as has for some time been conjectured and this paper shows, with the proper normalization it is false for the convex case.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 60 , Issue 4 , October 1964 , pp. 821 - 845
Copyright
Copyright © Cambridge Philosophical Society 1964

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References

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