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By Professor Dr. Rolf Nevanlinna (auth.), Professor Dr. B. Eckmann, Professor Dr. B. L. van der Waerden (eds.)

ISBN-10: 3642855903

ISBN-13: 9783642855900

ISBN-10: 364285592X

ISBN-13: 9783642855924

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5. On the Level Lines of the Harmonic Measure 33 The harmonic measure of a boundary arc at a point z is equal to 21n times the angle enclosed by the h-lines running from the end points of the arc to z. § 5. 1. : IX is a proper subarc of the boundary, w(z, IX, G) = A are circular arcs which join the end points of IX. It follows from this by conformal mapping that the system of level lines exhibits similar behavior when IX is a boundary arc of a region G bounded by the Jordan curve r: The lines K;.

We thus also take into consideration the possibility that the "region" Aw may consist solely of the arcs 1 2 "'w· § 1. The Principle of Harmonic Measure 39 is harmonic and single-valued inc:. Regarding the boundary points z* there are four cases to consider. 1. z* lies within G, and therefore belongs to the set Oi,. Here w{z*,

Ex, by the function z' = z2 , which carries [z[ <:::; 1 onto [z' [ < 1 and

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Analytic Functions by Professor Dr. Rolf Nevanlinna (auth.), Professor Dr. B. Eckmann, Professor Dr. B. L. van der Waerden (eds.)

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