ああ、いま改めて読むと Bulletin of the Calcutta Mathematical Society 49 (1957) Senguptaより ”・・・ 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).”
なんてありますね。”at least one of the four Dini derivates of f is infinite”が、貴方の定理に近いかな？ ”Then E is co-meager in R (i.e. the complement of a first category set).”か・・ これか、これに近い文献を読まないことには、訳わからんな
えーと、Meagre setか・・ ”E is co-meager in R”が、イメージできんな・・（＾＾
前提a)(連続不連続が稠密)を、b)(連続とディニ微分発散が稠密な組み合わせ)に、緩和しても・・ a) f is continuous and discontinuous are each dense in R. ↓ b) f is continuous and the E *) are each dense in R. ( *)the set of points at which f is continuous and where at least one of the four Dini derivates of f is infinite.)
