24 | 09 | 2017

vasile1

About Vasile Ene
Links
Contact

This email address is being protected from spambots. You need JavaScript enabled to view it.

Article 46

Theorems of Lusin type

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

Mathematical reviews subject classification: 26A46.

 

Abstract

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 ].