Examples of Ε-exhaustive Pathological Submeasures

@inproceedings{Farah2003ExamplesO,
  title={Examples of Ε-exhaustive Pathological Submeasures},
  author={Ilijas Farah and A submeasure},
  year={2003}
}
A submeasure θ on a Boolean algebra B is pathological if it does not dominate a positive finitely additive functional. It is ε-exhaustive if every sequence {An} of pairwise disjoint sets in B satisfies lim supn θ(An) ≤ ε. It is exhaustive if it is 0-exhaustive. It is normalized if θ(1B) = 1. Question 1. Is there a normalized exhaustive pathological submeasure on the algebra of clopen subsets of the Cantor space? 

From This Paper

Topics from this paper.

Citations

Publications citing this paper.
Showing 1-2 of 2 extracted citations

References

Publications referenced by this paper.
Showing 1-7 of 7 references

A simple example of a pathological submeasure

  • M. Talagrand
  • Mathematische Annalen, 252:97–102
  • 1980
Highly Influential
5 Excerpts

Measure Theory

  • D. H. Fremlin
  • volume 3. Torres–Fremlin
  • 2002
2 Excerpts

Maharam’s problem

  • J. W. Roberts
  • Proceedings of the Orlitz memorial conference
  • 1991
3 Excerpts

The Maharam problem

  • N. J. Kalton
  • In G. Choquet et al., editors, Séminaire…
  • 1988
1 Excerpt

Measurable cardinals and analytic games

  • D. A. Martin
  • Fund. Math.,
  • 1970
1 Excerpt

An algebraic characterization of measure algebras

  • D. Maharam
  • Annals of mathematics, 48:154–167
  • 1947
1 Excerpt

Similar Papers

Loading similar papers…