We show that if a homeomorphism f of a domain \( D \subset {\mathbb{R}^n} \), n ≥ 2, is a hyper-Q-homeomorphism with Q ∈ L 1loc , then f ∈ ACL. As a consequence, this homeomorphism has partial derivatives and an approximation differential almost everywhere.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 62, No. 1, pp. 139–144, January, 2010.
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Kovtonyuk, D.A. On the theory of hyper-Q-homeomorphisms. Ukr Math J 62, 155–161 (2010). https://doi.org/10.1007/s11253-010-0340-8
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DOI: https://doi.org/10.1007/s11253-010-0340-8