Abstract
The following assertion is proved: letf:B→Rn 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\((i,\frac{{\partial fi}}{{\partial xj}}(i,j = 1,2,...,n)\) are summable with respect to B with degreeα (1< α <- n). Then the mappingf has angular boundary values everywhere on the boundary of the sphere with the possible exception of a set ofα-capacity zero.
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