期刊名称：International Journal of Differential Equations and Applications
印刷版ISSN：1311-2872
出版年度：2005
卷号：10
期号：2
DOI：10.12732/ijdea.v10i2.192
语种：English
出版社：International Journal of Differential Equations and Applications
摘要：Let $(X,\|.\|,\vartheta)$ be a bitopological vector space suchthat $(X,\vartheta)$ is a topological vector space, $(X,\|.\|)$ isa reflexive normed space, the unit ball ${\cal B}_1(X)$ is closedin $(X,\vartheta)$ and sequentially complete under the topology$\vartheta$. Let $I=[\alpha,\beta]$ be an interval of $R$. Denoteby $l(X_{\vartheta},R)$ the space of all sequentially continuouslinear mapping from $X_\vartheta$ to $R$.We prove that if a subset ${\cal K}$ of$L^1(I,(X_\vartheta,\|.\|))$ is sequentially relativelycompact in$(L^1(I,(X_\vartheta,\|.\|)),\sigma(L^1(I,(X_\vartheta,\|.\|)),L^{\infty}(I,(l(X_{\vartheta},R),\|.\|_{X'}))))$,\linebreak then it is weakly uniformly integrable.
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