Kurepa's Hypothesis and a problem of Ulam on families of measures

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Abstract

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 languageEnglish (US)
Pages (from-to)41-57
Number of pages17
JournalMonatshefte für Mathematik
Volume81
Issue number1
DOIs
StatePublished - Mar 1 1976

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