Article 4

A study of Foran's conditions A(N) and B(N) and his class $\small{\mathcal F}$

Real Analysis Exchange 10 (1985), 194-212

Mathematical reviews subject classification: 26A45, 26A46, 26A39

Abstract

In this paper we show some interesting properties of Foran's class of functions $\small{\mathcal F}$ (see An extension of the Denjoy integral, Proc. Amer. Math. Soc., 49 (1975), 359-365).

Then we introduce a class $\small{\mathcal E}$ of continuous functions that strictly contains the class $\small{\mathcal F}$ .

The basic properties of the new class are established in Chapter V of the present paper.

All the properties are illustrated by constructive examples.