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Generalized Hausdorff dimension

Published online by Cambridge University Press:  26 February 2010

P. R. Goodey
P. R. Goodey
Affiliation:
Department of Mathematics, Royal Holloway College, Englefield Green, Surrey.
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Extract

It is natural to say that a set S in a metric space has infinite generalized Hausdorff dimension if there is no Hausdorff measure Λh with Λh(S) = 0. In this note we study such sets. We first need some definitions.

We say that h(x) is a Hausdorff measure function if it satisfies the conditions:

Type
Research Article
Information
Mathematika , Volume 17 , Issue 2 , December 1970 , pp. 324 - 327
Copyright
Copyright © University College London 1970

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References

1.Hausdorff, F., “Dimension und aüsseres Mass”, Math. Annalen, 79 (1918), 157–179.CrossRefGoogle Scholar
2.Besicovitch, A. S., “On the definition of tangents to sets of infinite linear measure”, Proc. Camb. Phil. Soc., 52 (1956), 20–29.CrossRefGoogle Scholar
3.Rogers, C. A., Hausdorff measures (Cambridge, 1970).Google Scholar
4.Taylor, A. E., Introduction to functional analysis (New York, 1964).Google Scholar