A new characterization of Buczolich's upper semicontinuously integrable functions.

Abstract

It is shown that if $f$ is Henstock-Kurzweil integrable on a compact interval $E$ in ${\mathbb R}^m$, then $f$ is upper semicontinuously integrable on $E$ if and only if there exists an increasing sequence $\{X_n\}$ of closed sets whose union is $E$, and $f |_{X_n}$ is bounded for each positive integer $n$.