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Non-Averaging Sets, Dimension and Porosity

Published online by Cambridge University Press:  20 November 2018

James Foran
James Foran*
Affiliation:
University of Missouri Kansas City, MO 64110
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Abstract

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A subset of the line is called non-averaging if, whenever two points belong to the set, their average does not. This paper provides an example of a closed set which is small in the sense that it is non-averaging and has porosity 1 at each of its points and yet large in the sense that its Hausdorff dimension is 1.

Keywords

26A2128A05
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 1 , 01 March 1986 , pp. 60 - 63
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Erdös, P. and Turan, P., On Some Sequences of Integers, Proc. Lond. Math. Soc. (2) 11 (1936), pp. 261–264.Google Scholar
2. Moser, L., On Non-Averaging Sets of Integers, Can. Jour, of Math. (1953), pp. 245—252.Google Scholar
3. Rogers, C. A., Hausdorff Measures, (Cambridge Univ. Press, Cambridge, 1970).Google Scholar