ON CONVERGENCE THEOREMS FOR SPACE QUASI-REGULAR MAPPINGS

Convergence problems are studied for quasiregular mappings in space. W e show the continuity of the injectivity radius for arbitrary continuo us discrete sense-preserving mappings and prove a space version of the Strebel convergence theorem for the local dilatation. We give the Ber s-Bojarski convergence theorem in terms of the matrix dilatation. We e stablish a sharp upper semicontinuity result for distortion coefficien ts in the mean. These theorems a re used to give some extensions of Li ouville's theorem (Lavrentiev-Reshetnyak).