Vol. 76, No. 1, 1978

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Meier type theorems for general boundary approach and σ-porous exceptional sets

Donald Charles Rung

Vol. 76 (1978), No. 1, 201–213

In this paper we are concerned with determining under what conditions equality is obtained between two different cluster sets of a function f at a point on the boundary of its domain. Specifically for functions defined in the unit disc D in the complex plane taking values in the extended plane we show that the generalized angle cluster set equals the generalized outer angular cluster set at all points of the boundary of D except possibly for a σ-porous set. The definition of both generalized cluster sets includes the usual Stolz angle definition but this result generalizes the known results. In addition the proof is shorter than proofs of less general results.

Mathematical Subject Classification 2000
Primary: 30D40
Received: 15 October 1977
Revised: 3 November 1977
Published: 1 May 1978
Donald Charles Rung