Journal article
Weak sequential convergence in Lp( μ, X)
Journal of mathematical analysis and applications, Vol.141(1), pp.72-83
07/01/1989
DOI: 10.1016/0022-247X(89)90206-0
Abstract
We provide some new results on the weak convergence of sequences or nets lying in
L
p
((
T, ∑,
μ),
X) ≡
L
p
(
μ,
X), 1 ⩽
p < ∞, i.e., the space of equivalence classes of
X-valued (
X is a Banach space) Bochner integrable functions on the finite measure space (
T, ∑,
μ). Our theorems generalize in several directions recent resuls on weak sequential convergence in
L
1(
μ,
X) obtained by M. A. Khan and M. Majumdar [
J. Math. Anal. Appl.
114 (1986), 569–573] and Z. Artstein [
J. Math. Econ.
6 (1979), 277–282], and they can be used to obtain dominated convergence results for the Aumann integral. Our results have useful applications in Economics and Game Theory.
Details
- Title: Subtitle
- Weak sequential convergence in Lp( μ, X)
- Creators
- Nicholas C Yannelis - University of Illinois Urbana-Champaign
- Resource Type
- Journal article
- Publication Details
- Journal of mathematical analysis and applications, Vol.141(1), pp.72-83
- DOI
- 10.1016/0022-247X(89)90206-0
- ISSN
- 0022-247X
- eISSN
- 1096-0813
- Publisher
- Elsevier Inc
- Language
- English
- Date published
- 07/01/1989
- Academic Unit
- Economics
- Record Identifier
- 9984380504002771
Metrics
2 Record Views