A General Convergence Theorem for Non‐Absolute Integrals | Zendy

Gordon Russell A. | Zendy

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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

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