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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



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.