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- W4300652893 abstract "A sequence ${f_n}$ of strongly-measurable functions taking values in a Banach space $X$ is scalarly null a.e. (resp. scalarly null in measure) if $x^*f_n rightarrow0$ a.e. (resp. $x^*f_n rightarrow 0$ in measure) for every $x^*in X^*$. Let $1le ple infty$. The main questions addressed in this paper are whether an $L_p(X)$-bounded sequence that is scalarly null a.e. will converge weakly a.e. (or have a subsequence which converges weakly a.e.), and whether an $L_p(X)$-bounded sequence that is scalarly null in measure will have a subsequence that is scalarly null a.e. The answers to these and other similar questions depend upon $p$ and upon the geometry of $X$." @default.
- W4300652893 created "2022-10-03" @default.
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- W4300652893 date "1996-04-04" @default.
- W4300652893 modified "2023-10-16" @default.
- W4300652893 title "On Various Modes of Scalar Convergence in L_0(X)" @default.
- W4300652893 doi "https://doi.org/10.48550/arxiv.math/9604212" @default.
- W4300652893 hasPublicationYear "1996" @default.
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