Abstract
Necessary and sufficient conditions are derived for the continuity and semiadditivity of the modulus of continuity of a functionf(x) given on a compact Ω in n-dimensional euclidean space.
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S. N. Kruzhkov, Nonlinear Partial Differential Equations [in Russian], Ch. 1, Moscow, Rotaprint VTs MGU (1969).
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Translated from Matematicheskie Zametki, Vol. 9, No. 5, pp. 495–500, May, 1971.
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Kolodii, I.M., Khil'debrand, F. Some properties of the modulus of continuity. Mathematical Notes of the Academy of Sciences of the USSR 9, 285–288 (1971). https://doi.org/10.1007/BF01094353
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DOI: https://doi.org/10.1007/BF01094353