# On some classes of continuous functions

### Real Analysis Exchange 11 (1986), 452-463.

#### Mathematical reviews subject classification: 26A30, 26A45, 26A46

## Abstract

In *An extension of the Denjoy integral* Proc. Amer. Math. Soc., **49** (1975), 359-365), Foran introduced the conditions

A(N) , B(N), and the class and in Article 4 we defined the condition E(N) and the class for a function on a set for some positive integer N.

In the present paper we construct a continuous function G_{N} which satisfies E(N+1) on a perfect set and which is E(N) on no portion of this set.

Moreover G_{N} has also the following properties:

and

We also construct a continuous function which satisfies Foran's condition N and which is not in.