A product convergence theorem for Henstock--Kurzweil integrals

Parasar Mohanty, Erik Talvila

Necessary and sufficient for ${\int }_a^{b}f{g}_n\to {\int }_a^{b}fg$ for all Henstock--Kurzweil integrable functions $f$ is that $g$ be of bounded variation, $g_n$ be uniformly bounded and of…