Premium
A General Convergence Theorem for Non‐Absolute Integrals
Author(s) -
Gordon Russell A.
Publication year - 1991
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/s2-44.2.301
Subject(s) - citation , convergence (economics) , mathematics , calculus (dental) , mathematical economics , library science , computer science , medicine , economics , economic growth , dentistry
summary:For the Kurzweil-Henstock integral the equiintegrability of a pointwise convergent sequence of integrable functions implies the integrability of the limit function and the relation\lim_{m \to\infty}\int_a^bf_m(s)\dd s = \int_a^b\lim_{m \to\infty}f_m(s)\dd s.Conditions for the equiintegrability of a sequence of functions pointwise convergent to an integrable function are presented. These conditions are given in terms of convergence of some sequences of integrals