Vol. 44, No. 2, 1973

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Hausdorff dimensions for compact sets in Rn

Robert Jay Buck

Vol. 44 (1973), No. 2, 421–434

A general Hausdorff dimension of sets in Rn is studied by considering the dependence of the dimension upon the size and shape, relative to the convex measure, of the elements in the covering family. The Hausdorff dimension of compact sets is related to the behavior of distribution functions of finite measures of compact support in Rn. A comparison of dimensions using diameter and Lebesgue measure is given in terms of the regularity of the shape of elements in the covering family.

Mathematical Subject Classification 2000
Primary: 28A75
Received: 7 September 1971
Revised: 15 September 1972
Published: 1 February 1973
Robert Jay Buck