2013•Journal of Nanchang UniversityRequires access

Calculation of Hausdorff Measures About a Class of Regular Hexahedrons

Nie Rao-ron

Abstract

The problem of calculation of Hausdorff measures of a class of self-similar sets in a regular hexahedron was studied in this paper When the similitude ratios satisfied certain conditions,it was proved that the natural cover was the best shape for upper convex density It means that the natural cover was a best one As a result,the exact value of Hausdorff measure of this class of self-similar sets is (3)~(1/2)s,where s is Hausdorff dimension.

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Key concepts: Mathematics, Hausdorff dimension, Hausdorff measure, Outer measure, Hausdorff distance, Hausdorff space, Urysohn and completely Hausdorff spaces, Class (philosophy)