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.v10i2.187
语种：English
出版社：International Journal of Differential Equations and Applications
摘要：We consider a bitopological vector space $(X,\vartheta,\|.\|)$, where $(X,\vartheta)$ is a topological vector space, and $\|.\|$ is a norm defined on $X$. We give some properties of the Bochner integral with respect to the pair of topologies $(\vartheta,\|.\|)$, and we introduce a special class of integrable functions denoted $L^p(E,(X_{\vartheta},\|.\|))$, which contains the usual Lebesgue space $L^p(E,(X,\|.\|))$. Next, we give an example which shows that the canonical injection of\linebreak $L^p(E,(X,\|.\|))$ into $L^p(E,(X_{\vartheta},\|.\|))$ is in general strict.
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