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Article 17

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.