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harmonic measure

   Also found in: Wikipedia 0.01 sec.
harmonic measure [här¦män·ik ′mezh·ər]
(mathematics)
LetDbe a domain in the complex plane bounded by a finite number of Jordan curves Γ, and let Γ be the disjoint union of α and β, where α and β are Jordan arcs; the harmonic measure of α with respect toDis the harmonic function onDwhich assumes the value 1 on α and the value 0 on β.
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The topics include Brownian motion and harmonic measure in conic sections, the sharpness of certain approach regions, integral representation for space-time excessive functions, hyperbolic Riemann surfaces without unbounded positive harmonic functions, and a vanishing theorem on the point- wise defect of a rational iteration sequence for moving targets.
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