Remarks on measurable Boolean algebras and sequential cardinals

G. Plebauek

Fundamenta Mathematicae (1993)

  • Volume: 143, Issue: 1, page 11-22
  • ISSN: 0016-2736

Abstract

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The paper offers a generalization of Kalton-Roberts' theorem on uniformly exhaustive Maharam's submeasures to the case of arbitrary sequentially continuous functionals. Applying the result one can reduce the problem of measurability of sequential cardinals to the question whether sequentially continuous functionals are uniformly exhaustive.

How to cite

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Plebauek, G.. "Remarks on measurable Boolean algebras and sequential cardinals." Fundamenta Mathematicae 143.1 (1993): 11-22. <http://eudml.org/doc/211988>.

@article{Plebauek1993,
abstract = {The paper offers a generalization of Kalton-Roberts' theorem on uniformly exhaustive Maharam's submeasures to the case of arbitrary sequentially continuous functionals. Applying the result one can reduce the problem of measurability of sequential cardinals to the question whether sequentially continuous functionals are uniformly exhaustive.},
author = {Plebauek, G.},
journal = {Fundamenta Mathematicae},
keywords = {Mazur functional; -complete Boolean algebra; sequential cardinals},
language = {eng},
number = {1},
pages = {11-22},
title = {Remarks on measurable Boolean algebras and sequential cardinals},
url = {http://eudml.org/doc/211988},
volume = {143},
year = {1993},
}

TY - JOUR
AU - Plebauek, G.
TI - Remarks on measurable Boolean algebras and sequential cardinals
JO - Fundamenta Mathematicae
PY - 1993
VL - 143
IS - 1
SP - 11
EP - 22
AB - The paper offers a generalization of Kalton-Roberts' theorem on uniformly exhaustive Maharam's submeasures to the case of arbitrary sequentially continuous functionals. Applying the result one can reduce the problem of measurability of sequential cardinals to the question whether sequentially continuous functionals are uniformly exhaustive.
LA - eng
KW - Mazur functional; -complete Boolean algebra; sequential cardinals
UR - http://eudml.org/doc/211988
ER -

References

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  1. [1] M. Antonovskiĭ and D. Chudnovsky, Some questions of general topology and Tikhonov semifields II, Russian Math. Surveys 31 (1976), 69-128. 
  2. [2] I. Anderson, A First Course in Combinatorial Mathematics, Clarendon Press, 1974. Zbl0268.05001
  3. [3] R. Engelking, On functions defined on Cartesian products, Fund. Math. 59 (1966), 221-231. Zbl0158.41203
  4. [4] D. H. Fremlin, Consequences of Martin's Axiom, Cambridge Univ. Press, 1984. Zbl0551.03033
  5. [5] D. H. Fremlin, Measure algebras, in: Handbook of Boolean Algebras, J. D. Monk (ed.), North-Holland, 1989, Vol. III, Chap. 22. 
  6. [6] N. J. Kalton and J. W. Roberts, Uniformly exhaustive submeasures and nearly additive set functions, Trans. Amer. Math. Soc. 278 (1983), 803-816. Zbl0524.28008
  7. [7] H. J. Keisler and A. Tarski, From accessible to inaccessible cardinals, Fund. Math. 53 (1964), 225-306. Zbl0173.00802
  8. [8] J. K. Kelley, Measures on Boolean algebras, Pacific J. Math. 9 (1959), 1165-1177. Zbl0087.04801
  9. [9] A. Louveau, Progrès récents sur le problème de Maharam d'après N. J. Kalton et J. W. Roberts, Publ. Math. Univ. Pierre Marie Curie 66 (1983/1984). 
  10. [10] S. Mazur, On continuous mappings on Cartesian products, Fund. Math. 39 (1952), 229-238. Zbl0050.16802
  11. [11] G. Plebanek, On the space of continuous functions on a dyadic set, Mathematika 38 (1991), 42-49. Zbl0776.46019
  12. [12] G. Plebanek, On the Mazur Property and realcompactness in C(K), in: Topology, Measures and Fractals, Math. Res. 66, Akademie-Verlag, 1992, 27-36. Zbl0850.46019
  13. [13] M. Talagrand, A simple example of pathological submeasure, Math. Ann. 252 (1980), 97-102. Zbl0444.28003

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