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Weak sequential convergence in Lp( μ, X)
Journal article   Open access   Peer reviewed

Weak sequential convergence in Lp( μ, X)

Nicholas C Yannelis
Journal of mathematical analysis and applications, Vol.141(1), pp.72-83
07/01/1989
DOI: 10.1016/0022-247X(89)90206-0
url
https://doi.org/10.1016/0022-247x(89)90206-0View
Published (Version of record) Open Access

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.

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