On Trigonometric Series and Primitive Functions

摘要

It is proved that any measurable, finite function f(x) has a smooth primitive F(x), i.e. there is a function F(x) such that F'(x) = f(x) almost everywhere, and particularly ω(δ; F) = o(δ In δ). This is an improvement of N. N. Luzin's theorem which states just the continuity of the primitive F(x).