After a short discussion of the first application of measure theoretic tools to economics we show that it is consistent relative to the usual axioms of set theory that there exists no nonatomic probability space of power less than the continuum. This together with other results shows that Aumann's continuum-of-agents methodology provides a sound framework at least for the cooperative theory.
There are, however, other problems in economics where, without further assumptions, the continuum may be the best model of large societies.
@article{urn:eudml:doc:38859,
title = {Some problems of measure theory which are related to economic theory.},
journal = {Stochastica},
volume = {6},
year = {1982},
pages = {305-320},
zbl = {0519.90030},
mrnumber = {MR0705768},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38859}
}
Skala, Heinz J. Some problems of measure theory which are related to economic theory.. Stochastica, Tome 6 (1982) pp. 305-320. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38859/