The Hausdorff Dimension Distribution of Finite Measures in Euclidean Space
- 1 December 1986
- journal article
- Published by Canadian Mathematical Society in Canadian Journal of Mathematics
- Vol. 38 (6) , 1459-1484
- https://doi.org/10.4153/cjm-1986-071-9
Abstract
Let E be a Borel set of RN. The α-outer Hausdorff measure of E has been defined to be where and each Bi is a closed ball. d(Bi) denotes the diameter of Bi.It is easily seen that the same value Hα(E) is obtained if we consider coverings of E by open balls or by balls which may be either open or closed.By dim(E) we will mean the usual Hausdorff-Besicovitch dimension of E, whereKeywords
This publication has 1 reference indexed in Scilit:
- Probability Theory IIPublished by Springer Nature ,1978