Measurability of Peano derivates and approximate Peano derivates (Q1898982)

The authors fill a gap in the theory of Peano and approximate Peano derivatives of measurable functions by showing that if one of these derivatives of order \(k\) exists on a set \(E_k\), then \(E_k\) is measurable and the derivative is measurable on \(E_k\); further the extreme derivates of order \(k + 1\) are also measurable on \(E_k\). In particular, the set of points where one of these derivatives exists is measurable and the derivative itself is measurable on that set.