Article 3

On Lusin's condition (N)

(Asupra conditiei (N) a lui Lusin - in Romanian)

Studii si Cercetari Matematice, 36 (1984), no. 22, 83-85.

Mathematical reviews subject classification: 26A30

Abstract

The intention of this article is to construct:

• an increasing, unbounded sequence of continuous real functions G_n that satisfy Lusin's condition (N) on [0,1], and
• a decreasing, unbounded sequence of continuous real functions H_m that satisfy Lusin's condition (N) on [0,1],

such that G'_n = H'_m a.e. on [0,1] for any positive integers m and n.