`Duality' of the Nikodym property and the Hahn property: Densities defined by sequences of matrices

DOI10.1016/j.jmaa.2011.03.017zbMath1221.46006OpenAlexW1967463123MaRDI QIDQ534741

Johann Boos, Toivo Leiger

Publication date: 10 May 2011

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2011.03.017

zbMATH Keywords

strong summabilitydensities defined by matrices or by sequences of matricesHahn propertiesNikodým propertystrongly nonatomic densities

Mathematics Subject Classification ID

Classes of sets (Borel fields, (sigma)-rings, etc.), measurable sets, Suslin sets, analytic sets (28A05) Matrix methods for summability (40C05) Sequence spaces (including Köthe sequence spaces) (46A45)

Related Items (3)

On the work of Lech Drewnowski ⋮ An application of LF-spaces to Silverman-Toeplitz type theorems ⋮ Hahn spaces in Fréchet spaces and applications to real sequence spaces

Cites Work

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• Generalizations of the Nikodym boundedness and Vitali--Hahn--Saks theorems
• Theorems of Toeplitz-Silverman type for maps defined by sequences of matrices
• An application of LF-spaces to Silverman-Toeplitz type theorems
• A generalization of the Nikodým boundedness theorem
• On some `duality' of the Nikodym property and the Hahn property
• Sequences of 0's and 1's
• Strongly nonatomic densities defined by certain matrices
• Stable Kneser hypergraphs and ideals in $\mathbb {N}$ with the Nikodým property
• Barrelled subspaces of spaces with subseries decompositions or Boolean rings of projections
• Approximation in Bounded Summability Fields

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