We construct a continuous function such that possesses -property, but does not have approximate derivative on a set of full Lebesgue measure. This shows that Banach’s Theorem concerning differentiability of continuous functions with Lusin’s property does not hold for -property. Some relevant properties are presented.
Stanisław Kowalczyk. Małgorzata Turowska. "On the Property ." Abstr. Appl. Anal. 2016 1 - 5, 2016. https://doi.org/10.1155/2016/1256906