Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-30T18:52:29.111Z Has data issue: false hasContentIssue false
  • English
  • Français

Property kα,n on Spaces with Strictly Positive Measure

Published online by Cambridge University Press:  20 November 2018

S. Argyros  and
N. Kalamidas
S. Argyros
Affiliation:
Athens University, Athens, Greece
N. Kalamidas
Affiliation:
Athens University, Athens, Greece
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we study intersection properties of measurable sets with positive measure in a probability measure space, or equivalently, intersection properties of open subsets on a compact space with a strictly positive measure.

The first result in this direction is due to Erdös and it is a negative solution to the problem of calibers on such spaces. In particular, under C.H., Erdös proved that Stone's space of Lebesque measurable sets of [0, 1] modulo null sets, does not have ℵ1-caliber.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 34 , Issue 5 , 01 October 1982 , pp. 1047 - 1058
Copyright
Copyright © Canadian Mathematical Society 1982

References

1. Argyros, S. and Negrepontis, S., Universal embeddings of la1 into C(X) and JL°°(M), Proceedings of Colloquium on Topology, Budapest (1978)./Google Scholar
2. Argyros, S. and Tsarpalias, A., Calibers of compact spaces, to appear in T.A.M.S.Google Scholar
3. Argyros, S., On compact spaces without strictly positive measure (to appear).Google Scholar
4. Comfort, W. and Negrepontis, S., Chain conditions in topology, Cambridge University Press (to appear)./Google Scholar
5. Erdôs, and Rado, , Intersection theorems for systems of sets, J. London Math. Soc. 44 (1969), 467–479./Google Scholar
6. Gaifman, H., Concerning measures on Boolean algebras, Pacific J. Math. 14 (1964), 61–73./Google Scholar
7. Galvin, F. and Hajnal, A. (manuscript).Google Scholar
8. Galvin, F., Chain conditions and products (to appear in Fund. Math.).Google Scholar
9. Hagler, J., On the structure of S and C(S) for S dyadic, T.A.M.S. 214 (1975), 415–427./Google Scholar
10. Kelley, J., Measures in Boolean algebras, Pacific J. Math. 9 (1959), 1165–1177./Google Scholar
11. Lacey, E., The isometric structure of classical Banach spaces, 208 (Springer-Verlag, Berlin, Heidelberg, New York)./Google Scholar
12. Maharam, D., On homogeneous measure algebras, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 108–11.Google Scholar