‘Duality’ of the Nikodym property and the Hahn property: Densities defined by sequences of matrices |
| |
Authors: | Johann Boos Toivo Leiger |
| |
Affiliation: | a Fakultät für Math. und Inf., FernUniversität in Hagen, 58084 Hagen, Germany b Matemaatika Instituut, Tartu Ülikool, EE 50090 Tartu, Estonia |
| |
Abstract: | The authors investigated in Boos and Leiger (2008) 5] the ‘duality’ of the Nikodym property (NP) of the set of all null sets of the density defined by any nonnegative matrix and the Hahn property (HP) of the strong null domain of it. In this paper, the investigation of the intimated duality is continued by considering densities defined by sequences of nonnegative matrices. These considerations are motivated by the known result that the ideal of the null sets of the uniform density has NP. In this context the general notion of S-convergence of double sequences (cf. Drewnowski, 2002 8]) containing Pringsheim convergence, Hardy convergence and uniform convergence of double sequences is used. |
| |
Keywords: | Hahn properties Nikodym property Strongly nonatomic densities Densities defined by matrices or by sequences of matrices Strong summability |
本文献已被 ScienceDirect 等数据库收录! |
|