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 ]](http://latex.codecogs.com/gif.latex?%5Csmall%5Cbigl%20%5B%7B%5Cmathcal%20B%7D%5Cbigr%20%5D "\small\bigl [{\mathcal B}\bigr ]")
,![\small\bigl [{\mathcal F}\bigr ]](http://latex.codecogs.com/gif.latex?%5Csmall%5Cbigl%20%5B%7B%5Cmathcal%20F%7D%5Cbigr%20%5D "\small\bigl [{\mathcal F}\bigr ]")
.
