%A ?. ?. ???????????
%J ??????????? ???????????? ??????
%T ????????? ????? ????? ?. ?. ????????? ?? ?????? ???????????????? ???????????
%X The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings
f ? W1,n
loc such that their outer dilatation KO(x, f) belongs to Ln?1
loc and the measure of the
set Bf of branching points of f is equal to zero have finite length distortion. In other words, the images
of almost all curves ? in the domain D under the considered mappings f : D ? Rn, n ? 2,
are locally rectifiable, f possesses the (N)-property with respect to length on ? , and, furthermore, the
(N)-property also holds in the inverse direction for liftings of curves. The results obtained generalize the
well-known Poletskii lemma proved for quasiregular mappings.
%N 7
%P 969-975
%V 61
%D 2009
%I ??????????? ???????? ????
%L zu213845