これに匹敵する結果は、>>41-42に書いたが ”Let f:R --> R be such that the sets of points at which f is continuous and discontinuous are each dense in R. Let E be the set of points at which f is continuous and where at least one of the four Dini derivates of f is infinite. Then E is co-meager in R (i.e. the complement of a first category set). This was proved in H. M. Sengupta and B. K. Lahiri, "A note on derivatives of a function", Bulletin of the Calcutta Mathematical Society 49 (1957), 189-191 [MR 20 #5257; Zbl 85.04502]. ”
つまり、一般な稠密性（但し、H. M. Sengupta and B. K. Lahiriは、可算非可算に関係なく） ”the sets of points at which f is continuous and discontinuous are each dense in R.”なのだが しかし、この discontinuous →リプシッツ連続でないという、上記１）の特性で、定理1.7は拡張されているのだ
