A bound of the exterior arcs for a univalent mapping

In this paper we consider the intersection of the circle ¦w|=x with the image of the disc ¦z|&#x2264;r, 0f(z)=z+c₂z²+... which is univalent analytic in ¦z|<1. Earlier I. E. Bazilevich proved that for xc^/er the measure of the above intersection does not exceed the measure of the intersection produced by the functionf ^*(z)=z/(1–z)², ¦=1. In this paper I. E. Bazilevich's ideas are used to strengthen some of his results.Translated from Matematicheskie Zametki, Vol. 18, No. 3, pp. 367–378, September, 1975.