Weak Sequential Convergence in L , ( p , X )
نویسنده
چکیده
We provide some new results on the weak convergence of sequences or nets lying in L,((T, & r), X) = L,(p, X), 1 <p < co, i.e., the space of equivalence classes of X-valued (X is a Banach space) Bochner integrable functions on the finite measure space ( r, z, I”). Our theorems generalize in several directions recent resuls on weak sequential convergence in L,(p, X) obtained by M. A. Khan and M. Majumdar [J. Mad Anal. Appl. 114 (1986), 569-5731 and Z. Artstein [J. Math. Econ. 6 (1979), 277-2821, 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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تاریخ انتشار 2003