For any given ε > 0 we construct an ε-exhaustive normalized pathological submeasure. To this end we use potentially exhaustive submeasures and barriers of finite subsets of ℕ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-4,
author = {Ilijas Farah},
title = {Examples of $\epsilon$-exhaustive pathological submeasures},
journal = {Fundamenta Mathematicae},
volume = {184},
year = {2004},
pages = {257-272},
zbl = {1069.28002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-4}
}
Ilijas Farah. Examples of ε-exhaustive pathological submeasures. Fundamenta Mathematicae, Tome 184 (2004) pp. 257-272. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm181-3-4/