Generalization of one Poletskii lemma to classes of space mappings

Abstract

n−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 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.