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.
