On the Property N-1

الملخص EN

We construct a continuous function f:[0,1]→R such that f possesses N-1-property, but f 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 (N) does not hold for N-1-property.

Some relevant properties are presented.