Hostname: page-component-78c5997874-v9fdk Total loading time: 0 Render date: 2024-11-05T11:45:35.602Z Has data issue: false hasContentIssue false
  • English
  • Français

ON TALAGRAND’S EXHAUSTIVE PATHOLOGICAL SUBMEASURE

Published online by Cambridge University Press:  12 December 2014

OMAR SELIM
OMAR SELIM*
Affiliation:
SCHOOL OF MATHEMATICS UNIVERSITY OF EAST ANGLIA, UK E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate Talagrand’s construction of an exhaustive pathological submeasure. We consider the forcing associated with this submeasure and we also begin an effort to explicitly describe this construction.

Keywords

03E7528A60Maharam algebraMeasure algebraSubmeasure
Type
Articles
Information
The Journal of Symbolic Logic , Volume 79 , Issue 4 , December 2014 , pp. 1046 - 1060
Copyright
Copyright © The Association for Symbolic Logic 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Balcar, B. and Jech, T., Weak distributivity, a problem of von Neumann and the mystery of measurability. Bulletin of Symbolic Logic, vol. 12 (2006), no. 2, pp. 241–266.CrossRefGoogle Scholar
Christensen, J. P. R., Some results with relation to the control measure problem, In Vector space measures and applications (Proc. Conf., Univ. Dublin, Dublin, 1977), II, Lecture Notes in Physics, vol. 77, Springer, Berlin, 1978, pp. 27–34.CrossRefGoogle Scholar
Dudley, R. M., Real analysis and probability, Second edition, Cambridge Studies in Advanced Mathematics, vol. 74, Cambridge University Press, Cambridge, 2002.Google Scholar
Farah, I., Examples of -exhaustive pathological submeasures. Funtamenta Mathematicae, vol. 181 (2004), no. 3, pp. 257–272.Google Scholar
Fremlin, D. H., Talagrand’s Example, Version 04/08/08, Available from: http://www.essex.ac.uk/maths/staff/fremlin/preprints.htm.Google Scholar
Fremlin, D. H., Measure algebras, Corrected second printing of the 2002 original, Measure theory, vol. 3, Torres Fremlin, Colchester, 2004.Google Scholar
Farah, I. and Zapletal, J., Between Maharam’s and von Neumann’s problems. Mathematical Research Letters, vol. 11 (2004), no. 5, 6, pp. 673–684.Google Scholar
Hall, P., On representatives of subsets. Journal of the London Mathematical Society, vol. 10 (1935), pp. 26–30.Google Scholar
Halmos, P., Measure Theory, D. Van Nostrand, New York, 1950.Google Scholar
Jech, T., Set theory: The third millennium edition, revised and expanded, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 2003.Google Scholar
Kechris, A. S., Classical descriptive set theory, Graduate Texts in Mathematics, vol. 156, Springer-Verlag, New York, 1995.Google Scholar
Koppelberg, S., Handbook of Boolean algebras (Donald Monk, J. and Bonnet, Robert, editors), vol. 1, North-Holland, Amsterdam, 1989.Google Scholar
Kalton, N. J. and Roberts, J. W., Uniformly exhaustive submeasures and nearly additive set functions. Transactions of the American Mathematical Society, vol. 278 (1983), vol. 2, pp. 803–816.Google Scholar
Kunen, K., Set theory: An introduction to independence proofs, Studies in Logic and the Foundations of Mathematics, vol. 102, North-Holland, Amsterdam, 1980.Google Scholar
Kunen, K., Random and Cohen reals, In Handbook of set-theoretic topology, North-Holland, Amsterdam, 1984, pp. 887–911.CrossRefGoogle Scholar
Maharam, D., An algebraic characterization of measure algebras. Annals of Mathematics (2), vol. 48 (1947), pp. 154–167.CrossRefGoogle Scholar
Roberts, J. W., Maharam’s problem, Proceedings of the Orlicz Memorial Conference (Kranz, Labuda, editors), 1991, unpublished.Google Scholar
Selim, O., Some observations and results concerning submeasures on Boolean algebras, Ph.D. thesis, University of East Anglia, 2012.Google Scholar
Talagrand, M., Maharam’s problem. Annals of Mathematics (2), vol. 168 (2008), no. 3, pp. 981–1009.Google Scholar
Zapletal, J., Forcing idealized, Cambridge Tracts in Mathematics, vol. 174, Cambridge University Press, Cambridge, 2008.Google Scholar