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Regulated functions appear in the works by J. Dieudonné [58, p. 139] and N. Bourbaki [32, p. II.4]. The raison d'être of regulated functions lies on the fact that every regulated function has a primitive, that is, there exists a continuous function such that almost everywhere in , in the sense of the Lebesgue measure. The interested reader may want to check this fact as described, for instance, by the group N. Bourbaki in [32, Corollaire I, p. II.6].