##  [Harmonic Measure Zero Set](/harmonic-measure-zero-set) 

  ##  [Harmonic Measure Zero Set](https://puremath.quantumdictionary.io/harmonic-measure-zero-set-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A subset E of the boundary ∂Ω of a domain Ω in which the harmonic measure ω^x(E) equals zero for a chosen reference interior point x (or for harmonic measure from every interior point); equivalently, E is charged with zero probability by Brownian motion started at x upon first exit of Ω.