1998•Real Analysis ExchangeRequires access

ON THE HAUSDORFF MEASURE OF A CLASS OF SELF-SIMILAR SETS

Jung

Abstract

We develop a new combinatorial method to estimate Hausdorff measures of various self-similar sets. This method can be applied to the evaluation of Hausdorff measures which are induced by various Hausdorff functions including power functions. Moreover, a few examples for evaluations of the lower and upper bounds of Hausdorff measures of uniform Cantor sets are introduced.

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