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/