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Exact Hausdorff measures of Cantor sets. (English) Zbl 1329.28019

The author investigates Hausdorff measures \(\mu_h\) on Cantor sets, i.e., compact, perfect, and totally disconnected subsets of \(\mathbb{R}\), where the gauge function \(h\) not only depends on the length of the covering intervals but also on their midpoints. For a class of regular enough Cantor sets it is shown that under this additional assumption a formula for the Hausdorff measure can be obtained. For three examples, the exact Hausdorff measure is computed.

MSC:

28A80 Fractals
28A78 Hausdorff and packing measures
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