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Capacities of certain Cantor sets

Authors
Journal
Indagationes Mathematicae
0019-3577
Publisher
Elsevier
Publication Date
Volume
8
Issue
2
Identifiers
DOI: 10.1016/s0019-3577(97)89123-9

Abstract

Abstract We prove a Nevanlinna-like criterion for positive capacity of Cantor-type sets K. Using this criterion, examples are constructed of such K with capacity zero such that the projections of the square K × K in all but two directions have positive capacity. We also construct a set of positive capacity whose projections in infinitely many directions have capacity zero.

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