On lower order of mappings with finite length distortion

For mappings of finite distortion actively investigated last 15--20 years, problems of a so-called lower order are discussed. It is proved that, mappings with finite length distortion $f:D\rightarrow {\Bbb R}^n,$ $n\ge 2,$ which have locally integrable other dilatation in degree $\alpha>n-1,$ and have a finite asymptotic value are of a uniformly lower bounded lower order.