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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 Gn that satisfy Lusin's condition (N) on [0,1], and
  • a decreasing, unbounded sequence of continuous real functions Hm 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.