## Real Analysis Exchange

### The Wide Denjoy Integral as the Limit of a Sequence of Stepfunctions in a Suitable Convergence

Vasile Ene

#### Abstract

In this paper we shall prove that a function $f:[a,b] \to \overline{{\mathbb R}}$ that is ${\mathcal D}$--integrable on $[a,b]$ can be defined as the limit of a ${\mathcal D}$-controlled convergent sequence of stepfunctions (see the second part of Theorem 2). In the last section we show that Ridder’s $\alpha$- and $\beta$-integrals can also be defined as the limit of some controlled convergent sequences of stepfunctions (see Theorem 4).

#### Article information

Source
Real Anal. Exchange, Volume 23, Number 2 (1999), 719-734.

Dates
First available in Project Euclid: 14 May 2012