Completeness of \(L_p\)-spaces in the finitely additive setting and related stories

DOI10.1006/jmaa.2000.6946zbMath0976.46017OpenAlexW2070541788MaRDI QIDQ1583962

Achille Basile, K. P. S. Bhaskara Rao

Publication date: 28 February 2001

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6946

zbMATH Keywords

completenessRadon-Nikodým derivativefinitely additive measureStone spacechargeHahn decompositionconvergence hazilyRadon-Nikodým metric

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Spaces of measures, convergence of measures (28A33) Vector-valued measures and integration (46G10) Open mapping and closed graph theorems; completeness (including (B)-, (B_r)-completeness) (46A30)

Related Items (9)

Properties of functions on a bounded charge space ⋮ Finitely additive representation of \(L^{p}\) spaces ⋮ On the additive property of finitely additive measures ⋮ Measurability of functions mapping a charge space into a uniform space ⋮ On a relation between density measures and a certain flow ⋮ Large games and the law of large numbers ⋮ Density measures and additive property ⋮ On the comparison of Aumann and Bochner integrals ⋮ The finitely additive integral of multifunctions with closed and convex values

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• Completeness of $L^p$-spaces over finitely additive set functions
• On the completeness of $ℒ_p$-spaces over a charge

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