We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
THE MCSHANE INTEGRAL IN THE LIMIT.
- Authors
Sayyad, Redouane
- Abstract
We introduce the notion of the McShane integral in the limit for functions defined on a σ-finite outer regular quasi Radon measure space (S;∈; T ; µ) into Banach space X and we study its relation with the generalized McShane integral introduced by D. H. Fremlin [2]. It is shown that if a function from S into X is McShane integrable in the limit on S and scalarly locally λ-upper McShane bounded for some λ > 0, then it is McShane integrable on S. On the other hand, we prove that if X-valued function is McShane integrable in the limit on S, then it is McShane integrable on each member of an increasing sequence (Sl)l≥1 of measurable sets of finite measure with union S. We also prove a Beppo Levi's version Theorem for this new integral.
- Subjects
INTEGRALS; LIMITS (Mathematics); MATHEMATICAL functions; RADON measures; BANACH spaces; MATHEMATICAL sequences
- Publication
Real Analysis Exchange, 2017, Vol 42, Issue 2, p283
- ISSN
0147-1937
- Publication type
Article
- DOI
10.14321/realanalexch.42.2.0283