, Volume 61, Issue 7, pp 1151-1157
Date: 03 Dec 2009

Generalization of one Poletskii lemma to classes of space mappings

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access

The paper is devoted to investigations in the field of space mappings. We prove that open discrete mappings fW 1,n loc such that their outer dilatation K O (x, f) belongs to L n−1 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.