|ISSN 1088-6826(online) ISSN 0002-9939(print)|
Functions with a concave modulus of continuity
Abstract: In , C. Goffman proved that, if is a modulus of continuity, then the set of all functions f in such that (m denotes Lebesgue measure) for all g in , the set of all functions in having as a modulus of continuity, is residual in . In the present article, we prove that, if is a concave modulus of continuity and , then the set of all functions f in such that for all g in is residual in . Using this result, we show that, if , then there are functions in which satisfy a Hölder condition of exponent such that for all g in which satisfy a Hölder condition of exponent .
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