Compactness in spaces of p-integrable functions with respect to a vector measure
DOI:
https://doi.org/10.12775/TMNA.2015.030Keywords
Banach function space, vector measure integration, compactnessAbstract
We prove that, under some reasonable requirements, the unit balls of the spaces $L^p(m)$ and $L^\infty(m)$ of a vector measure of compact range $m$ are compact with respect to the topology $\tau_m$ of pointwise convergence of the integrals. This result can be considered as a generalization of the classical Alaoglu Theorem to spaces of $p$-integrable functions with respect to vector measures with relatively compact range. Some applications to the analysis of the Saks spaces defined by the norm topology and $\tau_m$ are given.Downloads
Published
2015-06-01
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1.
RUEDA, Pilar and SÁNCHEZ-PÉREZ, Enrique A. Compactness in spaces of p-integrable functions with respect to a vector measure. Topological Methods in Nonlinear Analysis. Online. 1 June 2015. Vol. 45, no. 2, pp. 641 - 653. [Accessed 19 April 2024]. DOI 10.12775/TMNA.2015.030.
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