Examples on harmonic measure and normal numbers

Author:
Jang-Mei Wu

Journal:
Proc. Amer. Math. Soc. **95** (1985), 211-216

MSC:
Primary 30C85; Secondary 31A15

DOI:
https://doi.org/10.1090/S0002-9939-1985-0801325-X

MathSciNet review:
801325

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Abstract: Suppose that is a bounded set in , , with positive capacity. Add to a disjoint set so that is closed, and let . Under what conditions on the added set do we have harmonic measure ? It turns out that besides the size of near , the location of relative to also plays an important role. Our example, based on normal numbers, stresses this fact.

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DOI:
https://doi.org/10.1090/S0002-9939-1985-0801325-X

Article copyright:
© Copyright 1985
American Mathematical Society