30 | 05 | 2024


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Article 46

Theorems of Lusin type

An. St. Univ. Ovidius Constanta 6 (1998), no. 2, 43-46.

Mathematical reviews subject classification: 26A46.



In this paper, using the Romanovski Lemma and the Baire Category Theorem, the author proves the following Lusin type theorem:

If F:[a,b] → R is a [VBG] function on [a,b], then there is a closed chain {Pn}n such that all FPn are VB on [a,b].


The question is if this theorem remains true for the following classes of functions:

  • [ACG],
  • ACG,
  • VB*G = [VB*G],
  • AC*G,
  • [CG],
  • [CiG],
  • [VBnG],
  • [ACnG],
  • \small\bigl [{\mathcal B}\bigr ],
  • \small\bigl [{\mathcal F}\bigr ].