On the theory of hyper-$Q$-homeomorphisms

Abstract

We show that if a homeomorphism $f$ of a domain $D ⊂ R^n,\; n ≥ 2$, is a hyper-$Q$-homeomorphism with $Q ∈ L_{\text{loc}^1$ , then $f ∈ ACL$. As a consequence, this homeomorphism has partial derivatives and an approximation differential almost everywhere.