A note on equivalent interval covering systems for Hausdorff dimension on ℝ
The Hausdorff dimension of a set in ℝ 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 dimens...
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| Format: | Article |
| Language: | English |
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Hindawi Limited
1988-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S016117128800078X |
| Summary: | The Hausdorff dimension of a set in ℝ 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. |
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| ISSN: | 0161-1712 1687-0425 |