History
Steffens (2006, p. 160) attributes the first usage of omega for the modulus of continuity to Lebesgue (1909, p. 309/p. 75) where omega refers to the oscillation of a Fourier transform. De la Vallée Poussin (1919, pp. 7-8) mentions both names (1) "modulus of continuity" and (2) "modulus of oscillation" and then concludes "but we choose (1) to draw attention to the usage we will make of it".
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