Poincaré studied with Hermite, who famously in a letter 1893 to Stieltjes wrote „I turn with terror and horror from this lamentable scourge of continuous functions with no derivative.“ Poincaré himself is often quoted „Heretofore when a new function was invented it was for some practical end; today they are invented expressly to put at fault the reasoning of our fathers; and one will never get more from them than that.“ Of course these quotes are older than the Lebesgue integral, though they may explain why integration of pathological functions was not considered to be important by Poincaré and other French mathematicians.

Poincaré studied with Hermite, who famously in a letter 1893 to Stieltjes wrote „I turn with terror and horror from this lamentable scourge of continuous functions with no derivative.“ Poincaré himself is often quoted „Heretofore when a new function was invented it was for some practical end; today they are invented expressly to put at fault the reasoning of our fathers; and one will never get more from them than that.“ Of course these quotes are older than the Lebesgue integral, yet they may explain why integration of pathological functions was not considered to be important by Poincaré and other French mathematicians.