Lower semicontinuity of distortion coefficients for homeomorphisms of bounded $(1, \sigma)$-weighted $(q,p)$-distortion on Carnot groups

In this paper we study the locally uniform convergence of homeomorphisms with bounded $(1,\sigma)$-weighted $(q,p)$-distortion to a limit homeomorphism. Under some additional conditions we prove that the limit homeomorphism is a mapping with bounded $(1,\sigma)$-weighted $(q,p)$-distortion. Moreover, we obtain the property of lower semicontinuity of distortion characteristics of homeomorphisms.