Examples on harmonic measure and normal numbers

Jang Mei Wu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)211-216
Number of pages6
JournalProceedings of the American Mathematical Society
Issue number2
StatePublished - Oct 1985

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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