This article is cited in 6 papers

Extension of functions preserving the modulus of continuity

V. A. Milman

Institute of Technical Cybernetics, National Academy of Sciences of Belarus

Abstract: The problem of the extension of a real-valued function from a subset of a metric space to the entire space is treated. An extension operator preserving the modulus of continuity of a function is proposed and its properties are studied. An application to the problem of the trace of a locally Lipschitz function on a compact subset of a metric space is given.

UDC: 517.5

Received: 20.10.1994

DOI: 10.4213/mzm1496

 English version: Mathematical Notes, 1997, 61:2, 193–200

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