We study local interpolation properties and local supremum properties for a Boolean algebra. In particular, we present a new condition that is sufficient for the Nikodym property.
@article{bwmeta1.element.bwnjournal-article-cmv71i1p79bwm,
author = {Antonio Aizpuru},
title = {The Nikodym property and local properties of Boolean algebras},
journal = {Colloquium Mathematicae},
volume = {70},
year = {1996},
pages = {79-85},
zbl = {0857.28003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p79bwm}
}
Aizpuru, Antonio. The Nikodym property and local properties of Boolean algebras. Colloquium Mathematicae, Tome 70 (1996) pp. 79-85. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv71i1p79bwm/
[000] [1] A. Aizpuru, Relaciones entre propiedades de supremo y propiedades de interpolación en álgebras de Boole, Collect. Math. 39 (1988), 115-125.
[001] [2] A. Aizpuru, On the Grothendieck and Nikodym properties of Boolean algebras, Rocky Mountain J. Math. 22 (1992), 1-10. | Zbl 0755.06008
[002] [3] F. K. Dashiell, Nonweakly compact operators from order Cauchy complete CS lattices, with application to Baire classes, Trans. Amer. Math. Soc. 266 (1981), 397-413. | Zbl 0493.47017
[003] [4] F. J. Freniche, The Vitali-Hahn-Saks theorem for Boolean algebras with the subsequential interpolation property, Proc. Amer. Math. Soc. 92 (1984), 362-366. | Zbl 0529.28004
[004] [5] F. J. Freniche, Some classes of Boolean algebras related to the Vitali-Hahn-Saks and Nikodym theorems, communication at the Meeting on Boolean Algebras, Oberwolfach, 1985.
[005] [6] M. T. Gassó, Algebras with the local interpolation property, Rocky Mountain J. Math. 22 (1992), 181-196.
[006] [7] R. Haydon, A non-reflexive Grothendieck space that does not contain , Israel J. Math. 40 (1981), 65-73.
[007] [8] A. Moltó, On the Vitali-Hahn-Saks theorem, Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 163-173. | Zbl 0482.46016
[008] [9] W. Schachermayer, On some classical measure theoretic theorems for non--complete Boolean algebras, technical report, Linz University, 1978.
[009] [10] G. Seever, Measures on F-spaces, Trans. Amer. Math. Soc. 133 (1968), 267-280. | Zbl 0189.44902
[010] [11] M. Talagrand, Propriété de Nikodym et propriété de Grothendieck, Studia Math. 68 (1984), 165-171. | Zbl 0563.28003