Fine variation and fractal measures

G. A. Edgar
Department of Mathematics
The Ohio State University
Columbus, OH 43210   U.S.A.

(Version of October, 1994)

Real Analysis Exchange 20 (1995) 256-280

Note: The version of the paper available here has script fonts, unlike the published version (where all fonts tend to look alike).

Abstract

Thomson noted that (in the line) the Hausdorff measures can be considered to be fine variations for appropriate choices of derivation basis and set function. We show that this point of view remains interesting in a general separable metric space. Use of the ``centered ball'' basis yields an alternate description of the covering measures of Saint Raymond and Tricot. Use of a ``closed set'' basis yields the Hausdorff measures. This paper may be considered a counterpart of [5], where the corresponding study of the packing measure may be found.

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