TY - JOUR
T1 - Examples on harmonic measure and normal numbers
AU - Wu, Jang Mei
PY - 1985/10
Y1 - 1985/10
N2 - Suppose that F is a bounded set in Rm, m ≥ 2, with positive capacity. Add to F a disjoint set E so that E ∪ F is closed, and let D = Rm\(E∪F). Under what conditions on the added set E do we have harmonic measure u(F, D) = 0? It turns out that besides the size of E near F, the location of E relative to F also plays an important role. Our example, based on normal numbers, stresses this fact.
AB - Suppose that F is a bounded set in Rm, m ≥ 2, with positive capacity. Add to F a disjoint set E so that E ∪ F is closed, and let D = Rm\(E∪F). Under what conditions on the added set E do we have harmonic measure u(F, D) = 0? It turns out that besides the size of E near F, the location of E relative to F also plays an important role. Our example, based on normal numbers, stresses this fact.
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U2 - 10.1090/S0002-9939-1985-0801325-X
DO - 10.1090/S0002-9939-1985-0801325-X
M3 - Article
AN - SCOPUS:84968490642
SN - 0002-9939
VL - 95
SP - 211
EP - 216
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 2
ER -