Classifying Cantor Sets by their Fractal Dimensions

Details Classifying Cantor Sets by their Fractal Dimensions Classifying Cantor Sets by their Fractal Dimensions

2009-05-12

arxiv.org/abs/0905.1980v2

Mathematics

Classical Analysis and ODEs

10 pages, revised version. To appear in Proceedings of the AMS.

Scientific paper

In this article we study Cantor sets defined by monotone sequences, in the
sense of Besicovitch and Taylor. We classify these Cantor sets in terms of
their h-Hausdorff and h-Packing measures, for the family of dimension functions
h, and characterize this classification in terms of the underlying sequences.

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