Abstract
Let (X, d, μ) and (Y, d′, μ′) be metric spaces α-regular by Ahlfors with α > 0 and locally finite Borel measures μ and μ′, respectively. We consider the class ACSE of absolutely continuous functions on a.a. compact subsets E ⊂ X and establish the membership of mappings f: X → Y to a given class.
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The article is dedicated to the memory of Professor Bogdan Bojarski
Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 16, No. 1, pp. 2–9 January–March, 2019.
The present work was supported by the Nationa; Academy of Sciences of Ukraine in the frame of the scientific research project for young scientists “Geometric properties of metric spaces and mappings in Finsler spaces”. The authors are grateful also to Doctor of Phys.-Math. Sci. V. I. Ryazanov for the useful discussions and remarks.
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Afanas’eva, E.S., Bilet, V.V. Some properties of quasisymmetries in metric spaces. J Math Sci 242, 754–759 (2019). https://doi.org/10.1007/s10958-019-04513-5
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DOI: https://doi.org/10.1007/s10958-019-04513-5