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A note on equivalent interval covering systems for Hausdorff dimension on â„

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  • C. D. Cutler

Abstract

The Hausdorff dimension of a set in â„ is usually defined by considering countable coverings of the set by general intervals. In this note we establish sufficient conditions under which coverings whose members are restricted to a particular family g of intervals will produce the same value for dimension. A result of Billingsley is then employed to obtain a general technique for computing the dimensions of sets defined by certain types of generalized expansions. A specific example is included.

Suggested Citation

  • C. D. Cutler, 1988. "A note on equivalent interval covering systems for Hausdorff dimension on â„," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 11, pages 1-7, January.
    • Handle: RePEc:hin:jijmms:952768
    DOI: 10.1155/S016117128800078X
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