On the equivalence of two convergence theorems for the Henstock integral (Q1803983)

The main result of the paper says that \(\{f_ n\}\) is uniformly Henstock integrable on \([a,b]\) if and only if \(\{F_ n\}\), where \(F_ n=\int^ x_ a f_ n\), is generalized \(P\)-Cauchy on \([a,b]\). The paper is a continuation of author's previous one in J. Lond. Math. Soc., II. Ser. 44, No. 2, 301-309 (1991; Zbl 0746.26003). Another characterization of the uniform Henstock integrability has been given recently by \textit{J. Kurzweil} and \textit{J. Jarník} in Real Anal. Exch. 17, No. 1, 110-139 (1992; Zbl 0754.26003).