International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1988 / Article

Open Access

Volume 11 |Article ID 952768 | https://doi.org/10.1155/S016117128800078X

C. D. Cutler, "A note on equivalent interval covering systems for Hausdorff dimension on ", International Journal of Mathematics and Mathematical Sciences, vol. 11, Article ID 952768, 7 pages, 1988. https://doi.org/10.1155/S016117128800078X

A note on equivalent interval covering systems for Hausdorff dimension on

Received30 Sep 1987

Abstract

The Hausdorff dimension of a set in 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.

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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