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Functions continuous and singular with respect to a Hausdorff measure

Published online by Cambridge University Press:  26 February 2010

C. A. Rogers  and
S. J. Taylor
C. A. Rogers
Affiliation:
University College, London
S. J. Taylor
Affiliation:
Cornell University, and Birmingham University
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Extract

1. Introduction. Let I0 be a closed rectangle in Euclidean n-space, and let ℬ be the field of Borel subsets of I0. Let ℱ be the space of completely additive set functions F, having a finite real value F(E) for each E of ℬ, and left undefined for sets E not in ℬ. In recent work, we used Hausdorff measures in an attempt to analyze the set functions F of ℱ. If h(t) is a monotonic increasing continuous function of t with h(0) = 0, a measure h-m(E) is generated by the method first defined by Hausdorff [2].

Type
Research Article
Information
Mathematika , Volume 8 , Issue 1 , June 1961 , pp. 1 - 31
Copyright
Copyright © University College London 1961

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References

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