In [1], C. Goffman proved that, if σ is a modulus of continuity, then the set of all functions f in C [ 0, 1] such that m ( {x:f (x) = g (x)}) = 0 (m denotes Lebesgue measure) for all g in C (σ), the ...

Andrea Cianchi, Monia Randolfi, On the Modulus of Continuity of Weakly Differentiable Functions, Indiana University Mathematics Journal, Vol. 60, No. 6 (2011), pp. 1939-1973 ...