We prove that if Kurepa's Hypothesis holds, then on a set of cardinality א1, there does not exist a family of א1 non-trivial measures such that each subset is measurable with respect to at least one of them. We also strengthen a theorem of Erdös and Alaoglu on the non-existence of enumerable families of measures.
|Original language||English (US)|
|Number of pages||17|
|Journal||Monatshefte für Mathematik|
|State||Published - Mar 1 1976|