On a problem of Faure and Guénard. (English) Zbl 0969.26007

Ene, Vasile

Real Anal. Exch. 24(1998-99), No. 2, 885-888 (1999).

Summary: In [Real Anal. Exch. 22, No. 2, 626-637 (1996; Zbl 0941.26006)], C.-A. Faure and F. Guénard put the following problem: Characterize the Denjoy\(^*\)-integrable functions \(f\: [a,b] \rightarrow \overline {\mathbb R}\) that can be approximated by two Baire 1 functions \(g_{\varepsilon}\) and \(h_{\varepsilon}\), \(\varepsilon > 0\), that are \(\mathcal D^*\)-integrable. In the present article we show that this class of functions coincides with the class of all \(\mathcal D^*\)-integrable functions \(f\: [a,b]\rightarrow \overline {\mathbb R}\).

MSC:

26A39

Denjoy and Perron integrals, other special integrals

Keywords:

Denjoy\(^*\)-integral; Perron type integrals; Baire class 1

Citations:

Zbl 0941.26006