18 | 07 | 2018
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Theorems of Lusin type

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],
• $\small\bigl [{\mathcal B}\bigr ]$,
• $\small\bigl [{\mathcal F}\bigr ]$.
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