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Article 39

On a problem of Faure and Guenard

Real Analysis Exchange 24 (1998/9), No. 2, 885-888.

Mathematical reviews subject classification: 26A39. 



In Upper and lower approximation of Perron integrable functions (Real Analysis Exchange 22 (1996/7), no. 2, 626-637), Faure and Guenard put the following problem:

Characterize the Denjoy*-integrable functions f:[a,b] → R  that can be approximated by two Baire1 functions  gε and hε , ε > 0, that are Denjoy*-integrable.


In the present article we show that this class of functions coincides with the class of all Denjoy*-integrable functions f:[a,b] → R.