The Nikodym property and local properties of Boolean algebras

Antonio Aizpuru

Colloquium Mathematicae (1996)

  • Volume: 71, Issue: 1, page 79-85
  • ISSN: 0010-1354

Abstract

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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.

How to cite

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Aizpuru, Antonio. "The Nikodym property and local properties of Boolean algebras." Colloquium Mathematicae 71.1 (1996): 79-85. <http://eudml.org/doc/210429>.

@article{Aizpuru1996,
abstract = {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.},
author = {Aizpuru, Antonio},
journal = {Colloquium Mathematicae},
keywords = {Boolean algebra; Nikodým property},
language = {eng},
number = {1},
pages = {79-85},
title = {The Nikodym property and local properties of Boolean algebras},
url = {http://eudml.org/doc/210429},
volume = {71},
year = {1996},
}

TY - JOUR
AU - Aizpuru, Antonio
TI - The Nikodym property and local properties of Boolean algebras
JO - Colloquium Mathematicae
PY - 1996
VL - 71
IS - 1
SP - 79
EP - 85
AB - 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.
LA - eng
KW - Boolean algebra; Nikodým property
UR - http://eudml.org/doc/210429
ER -

References

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  1. [1] A. Aizpuru, Relaciones entre propiedades de supremo y propiedades de interpolación en álgebras de Boole, Collect. Math. 39 (1988), 115-125. 
  2. [2] A. Aizpuru, On the Grothendieck and Nikodym properties of Boolean algebras, Rocky Mountain J. Math. 22 (1992), 1-10. Zbl0755.06008
  3. [3] F. K. Dashiell, Nonweakly compact operators from order Cauchy complete C ( S ) lattices, with application to Baire classes, Trans. Amer. Math. Soc. 266 (1981), 397-413. Zbl0493.47017
  4. [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. Zbl0529.28004
  5. [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. 
  6. [6] M. T. Gassó, Algebras with the local interpolation property, Rocky Mountain J. Math. 22 (1992), 181-196. 
  7. [7] R. Haydon, A non-reflexive Grothendieck space that does not contain l ∞ , Israel J. Math. 40 (1981), 65-73. 
  8. [8] A. Moltó, On the Vitali-Hahn-Saks theorem, Proc. Roy. Soc. Edinburgh Sect. A 90 (1981), 163-173. Zbl0482.46016
  9. [9] W. Schachermayer, On some classical measure theoretic theorems for non- σ -complete Boolean algebras, technical report, Linz University, 1978. 
  10. [10] G. Seever, Measures on F-spaces, Trans. Amer. Math. Soc. 133 (1968), 267-280. Zbl0189.44902
  11. [11] M. Talagrand, Propriété de Nikodym et propriété de Grothendieck, Studia Math. 68 (1984), 165-171. Zbl0563.28003

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