NORM CONVERGENCE AND UNIFORM INTEGRABILITY FOR THE HENSTOCK-KURZWEIL INTEGRAL
Swartz · Real Analysis Exchange · 1998
We show that a uniformly integrable, pointwise convergent sequence of Henstock-Kurzweil integrable functions converges in the Alexiewicz norm. In particular, this implies that a sequence satisfying the conditions in the Dominated Convergence Theorem is norm convergent.