2003/06/10 by Parasar Mohanty, Mohanty, Parasar, Erik Talvila +1
Economics, Econometrics and Finance · Mathematics · #26A39 #46E30 #Advanced Banach Space Theory #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Stochastic processes and financial applications #math.CA #msc:26A39 #msc:46E30
paper · pdf · doi:10.48550/arxiv.math/0306175
See http://www.math.ualberta.ca/~etalvila/research.html. Real. Anal. Exchange (to appear)
arxiv created 2003/06/10 · openalex publication_date 2003/06/10 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Necessary and sufficient for ∫abfgn→ ∫abfg for all Henstock--Kurzweil integrable functions f is that g be of bounded variation, gn be uniformly bounded and of uniform bounded variation and, on each compact interval in (a,b), gn→ g in measure or in the L1 norm. The same conditions are necessary and sufficient for ‖f(gn-g)‖→ 0 for all Henstock--Kurzweil integrable functions f. If gn→ g a.e. then convergence ‖fgn‖→‖fg‖ for all Henstock--Kurzweil integrable functions f is equivalent to ‖f(gn-g)‖→ 0. This extends a theorem due to Lee Peng-Yee.