For map**s in metric spaces satisfying one inequality for the modulus of families of curves, we establish the property of lightness of the limit map**. It is shown that the uniform limit of these map**s is a light map**, whenever the majorant responsible for the distortion of the families of curves is of finite mean oscillation at any point. In addition, for one class of homeomorphisms of metric spaces, we prove theorems on the equicontinuity of the families of inverse map**s.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 7, pp. 952–967, July, 2018.
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Sevost’yanov, E.A., Skvortsov, S.A. On the Convergence of Map**s in Metric Spaces with Direct and Inverse Modulus Conditions. Ukr Math J 70, 1097–1114 (2018). https://doi.org/10.1007/s11253-018-1554-4
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DOI: https://doi.org/10.1007/s11253-018-1554-4