Boundary property of n-dimensional mappings with bounded distortion

The following assertion is proved: letf:BRⁿ be an arbitrary (in general, not single-sheeted) mapping with bounded distortion of an n-dimensional sphere B, satisfying the conditions: A) the setf(B) is bounded; B) the partial derivatives are summable with respect to B with degree (1< <- n). Then the mappingf has angular boundary values everywhere on the boundary of the sphere with the possible exception of a set of-capacity zero.Translated from Matematicheskie Zametki, Vol. 11, No. 2, pp. 159–164, February, 1972.