On the Alexiewicz topology of the Denjoy space (Q1374535)

The space \(H\) of all Denjoy-Perron integrable functions on \([a,b]\) endowed with the Alexiewicz norm \(|f|_H=\sup_{x}|\int_a^xf(t) dt|\) is the Denjoy space of \([a,b]\). The completion \(\mathcal H\) of \(H\) is also studied and some previous results of the first author concerning the characterization of relatively (weakly) compact subsets of \(H\) and \(\mathcal H\) are completed and enhanced in the paper.