Characterization of AC*G ∩ C, AC* ∩ Ci, AC and AC functions
Real Analysis Exchange 19 (1994), 491-510.
Mathematical reviews subject classification: 26A45, 26A46, 26A39.
Abstract
In connection with the study of AC*G functions, Lee Peng Yee introduced a condition which lies somewhere between AC and Lusin's condition (N), and it is called the strong Lusin condition.
This condition also appears in Gordon's Lemma 2 of A descriptive characterization of the generalization of the generalized Riemann integral (Real Analysis Exchange 15 (1989/90), 397-400).
In the article Kurzweil-Henstock integration and strong Lusin condition (Real Analysis Exchange 17 (1991/2), 25-26), Lee and Vyborny mentioned that this condition was also studied by Kurzweil, Jarnik and Schwabik.
Denoting this condition by YDo we show that:
YDo = AC*G ∩ C
on a closed interval (C = the continuous functions).
There are then given several characterizations for the classes AC*G ∩ Ci, AC and AC.
