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Let D denote the open unit disk in the complex plane and let C be the boundary of D. If, for a given complex-valued function f(z) defined in D, the existence of a subset M of C is known, with the linear measure of M equal to 2 π, as well as an estimate on the growth of |f/(z)| I on sequences in D which tends to a point of M, then such a result will be called a “statistical” result on order. This terminology is due to Lelong-Ferrand [3].