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Positively Infinite Singularities of a Superharmonic Function

Published online by Cambridge University Press:  22 January 2016

Kikuji Matsumoto
Kikuji Matsumoto*
Affiliation:
Mathematical Institute Nagoya University
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Let E be a compact set of logarithmic capacity zero in the complex plane. Then the following is well-known as Evans-Selberg’s theorem [1] [8]: there is a measure with support contained in E such that its logarithmic potential is positively infinite at each point of E. But such a potential does not exist for E of logarithmic positive capacity. Now suppose that E is contained in the circumference of the unit disc |z| < 1 and is of linear measure zero.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 31 , January 1968 , pp. 89 - 96
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

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