A product convergence theorem for Henstock--Kurzweil integrals
| dc.creator | Mohanty, Parasar | |
| dc.creator | Talvila, Erik | |
| dc.date | 2003-06-10 | |
| dc.date.accessioned | 2026-07-07T04:58:53Z | |
| dc.date.available | 2026-07-07T04:58:53Z | |
| dc.description | Necessary and sufficient for $\int_a^bfg_n\to \int_a^bfg$ for all Henstock--Kurzweil integrable functions $f$ is that $g$ be of bounded variation, $g_n$ be uniformly bounded and of uniform bounded variation and, on each compact interval in $(a,b)$, $g_n\to g$ in measure or in the $L^1$ norm. The same conditions are necessary and sufficient for $\|f(g_n-g)\|\to 0$ for all Henstock--Kurzweil integrable functions $f$. If $g_n\to g$ a.e. then convergence $\|fg_n\|\to\|fg\|$ for all Henstock--Kurzweil integrable functions $f$ is equivalent to $\|f(g_n-g)\|\to 0$. This extends a theorem due to Lee Peng-Yee. | |
| dc.description | See http://www.math.ualberta.ca/~etalvila/research.html. Real. Anal. Exchange (to appear) | |
| dc.identifier | https://arxiv.org/abs/math/0306175 | |
| dc.identifier | http://arxiv.org/abs/math/0306175 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/67762 | |
| dc.subject | Classical Analysis and ODEs | |
| dc.subject | 26A39; 46E30 | |
| dc.title | A product convergence theorem for Henstock--Kurzweil integrals | |
| dc.type | text |