See H. W. Ellis, 'Darboux properties and applications to nonabsolutely convergent integrals' Canad. Math. J., 3 (1951), 471-484, where the same concept is labelled as [CG] (for generalized continuity).
For a deeper exploration of Darboux properties and their relevance to nonabsolutely convergent integrals, consult H. W. Ellis's article in Canad. Math. J., vol. 3, 1951, pp. 471-484, where the concept is referred to as [CG] (generalized continuity).