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
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 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.
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