Characterization of Compact Subsets of $\mathcal{A}^p$ with Respect to Weak Topology

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dc.creatorAssa, Hirbod
dc.date2008-04-17
dc.date.accessioned2026-07-07T09:33:13Z
dc.date.available2026-07-07T09:33:13Z
dc.descriptionIn this brief article we characterize the relatively compact subsets of $\mathcal{A}^p$ for the topology $σ(\mathcal{A}^p,\mathcal{R}^q)$ (see below), by the weak compact subsets of $L^p$ . The spaces $\mathcal{R}^q$ endowed with the weak topology induced by $\mathcal{A}^p$, was recently employed to create the convex risk theory of random processes. The weak compact sets of $\mathcal{A}^p$ are important to characterize the so-called Lebesgue property of convex risk measures, to give a complete description of the Makcey topology on $\mathcal{R}^q$ and for their use in the optimization theory.
dc.description8 pages
dc.identifierhttps://arxiv.org/abs/0804.2873
dc.identifierhttp://arxiv.org/abs/0804.2873
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159058
dc.subjectProbability
dc.subjectFunctional Analysis
dc.titleCharacterization of Compact Subsets of $\mathcal{A}^p$ with Respect to Weak Topology
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