@article{Sevost’yanov_2009, title={Generalization of one Poletskii lemma to classes of space mappings}, volume={61}, url={https://umj.imath.kiev.ua/index.php/umj/article/view/3071}, abstractNote={The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings $f ∈ W^{1,n}_{\text{loc }$ such that their outer dilatation $K_O (x, f)$ belongs to $L^{n−1}_{\text{loc }$ and the measure of the set $B_f$ of branching points of $f$ is equal to zero have finite length distortion. In other words, the images of almost all curves $γ$ in the domain $D$ under the considered mappings $f : D → ℝ^n,\;n ≥ 2$, are locally rectifiable, $f$ possesses the $(N)$-property with respect to length on $γ$, 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.}, number={7}, journal={Ukrains’kyi Matematychnyi Zhurnal}, author={Sevost’yanov, E. A.}, year={2009}, month={Jul.}, pages={969-975} }