Dolzhenko formulated the
notion of “porosity” for a set, which has been shown to be highly useful in
investigations of the theory of cluster sets.
In this paper, we make use of this technique in order to generalize Meier’s
results [Math. Ann., 147 (1961), 328-344] to the direction including tangential
cases.
As an application, we prove a theorem with respect to the existence of Lusin
points.
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