Editing Modulus of continuity (section)

===Sublinear moduli, and bounded perturbations from Lipschitz===
A sublinear modulus of continuity can easily be found for any uniformly continuous function which is a bounded perturbation of a Lipschitz function: if ''f'' is a uniformly continuous function with modulus of continuity ω, and ''g'' is a ''k'' Lipschitz function with uniform distance ''r'' from ''f'', then ''f'' admits the sublinear modulus of continuity min{ω(''t''), 2''r''+''kt''}. Conversely, at least for real-valued functions, any special uniformly continuous function is a bounded, uniformly continuous perturbation of some Lipschitz function; indeed more is true as shown below (Lipschitz approximation).