International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 4, Pages 643-650
doi:10.1155/S016117128800078X
A note on equivalent interval covering systems for Hausdorff dimension on ℝ
C.D. Cutler
Department of Statistics and Actuarial Science, University of Waterloo, Ontario, Waterloo N2L 3G1, Canada
Abstract
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.