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Article 47

On some classes of functions related to Lusin's condition (N)

An. St. Univ. Ovidius Constanta 6 (1998), no. 2, 47-52.

Mathematical reviews subject classification: 26A45, 26A46, 26A21, 26A30.



Lusin's condition (N) has an important role in the theory of integration, since the classes of primitives for many nonabsolutely convergent integrals satisfy this condition.

In this paper we study some relations between 

  • Lusin's condition (N),
  • Foran's conditions (M) and (wN),
  • Saks' condition N+∞,   and
  • the conditions (M), (N), (wN)   (introduced by the author).