Hostname: page-component-6d856f89d9-4thr5 Total loading time: 0 Render date: 2024-07-16T07:25:20.864Z Has data issue: false hasContentIssue false
  • English
  • Français

Hausdorff measure functions

Published online by Cambridge University Press:  24 October 2008

P. R. Goodey
P. R. Goodey
Affiliation:
Department of Mathematics, Royal Holloway College, Englefield Green, Surrey
Get access Rights & Permissions [Opens in a new window]

Extract

In many contributions to the theory of Hausdorff measures, it has been the practice to place certain restrictions on the measure functions used. These restrictions usually ensure both the monotonicity and the continuity of the functions. The purpose of this work is to find conditions under which the restrictions of monotonicity and continuity may be relaxed. We shall be working mostly with sets in Euclidean space, although in the final theorem, we work in Hilbert space to show that some of our previous results do not generalize to this space. I am grateful to the referee for suggesting improvements in the proofs of the results.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 74 , Issue 1 , July 1973 , pp. 87 - 96
Copyright
Copyright © Cambridge Philosophical Society 1973

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Devies, R. O.A property of Hausdorff measure. Proc. Cambridge Philos. Soc. 52 (1956), 30–34.CrossRefGoogle Scholar
(2)Dvoretzky, A.A note on Hausdorff dimension functions. Proc. Cambridge Philos. Soc. 44 (1948), 13–16.CrossRefGoogle Scholar
(3)Hausdorff, F.Dimension und aüsseres Mass. Math. Ann. 79 (1918), 157–179.CrossRefGoogle Scholar
(4)Sion, M. and Sjerve, D.Approximation properties of measures generated by continuous set functions. Mathematika 9 (1962), 145–156.CrossRefGoogle Scholar