Hausdorff and Packing Measures of Balanced Cantor Sets

Hausdorff and Packing Measures of Balanced Cantor Sets

We estimate the \(h\)-Hausdorff and \(h\)-packing measures of balanced Cantor sets, and characterize the corresponding dimension partitions. This generalizes results known for Cantor sets associated with positive decreasing summable sequences and central Cantor sets.

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Veröffentlicht in:Real analysis exchange 2015, Vol.40 (1), p.113-128
Hauptverfasser: Hare, Kathryn, Ng, Ka-Shing
Format: Artikel
Sprache:eng
Schlagworte:
28A78
28A80
Cantor sets
cut-out sets
dimension functions
gauge functions
Hausdorff measures
packing measures
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Beschreibung
Zusammenfassung:We estimate the \(h\)-Hausdorff and \(h\)-packing measures of balanced Cantor sets, and characterize the corresponding dimension partitions. This generalizes results known for Cantor sets associated with positive decreasing summable sequences and central Cantor sets.
ISSN:0147-1937
1930-1219
DOI:10.14321/realanalexch.40.1.0113