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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Estimates of the harmonic measure of a continuum in the unit disk


Authors: Carl H. FitzGerald, Burton Rodin and Stefan E. Warschawski
Journal: Trans. Amer. Math. Soc. 287 (1985), 681-685
MSC: Primary 30C85; Secondary 31A15
MathSciNet review: 768733
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Abstract: The harmonic measure of a continuum in the unit disk is estimated from below in two ways. The first estimate is in terms of the angle subtended by the continuum as viewed from the origin. This result is a dual to the Milloux problem. The second estimate is in terms of the diameter of the continuum. This estimate was conjectured earlier as a strengthening of a theorem of D. Gaier. In preparation for the proofs several lemmas are developed. These lemmas describe some properties of the Riemann mapping function of a disk with radial incision onto a disk.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0768733-1
PII: S 0002-9947(1985)0768733-1
Article copyright: © Copyright 1985 American Mathematical Society