Direct products of quasiregular mappings

Abstract

We prove that direct products of two quasiregular mappings are quasiregular under certain conditions of compatibility. Such a condition has been introduced by A.P. Karmazin for direct products of two quasiconformal homeomorphisms. Instead of the Markushevich–Pesin definition he used, we start with Reshetnyak's one, which allows us to consider normal neighborhoods, to establish properties of their direct products and to define the compatibility.