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

Karel Prikry

doi:10.1007/BF01473613

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

Karel Prikry

School of Mathematics

Research output: Contribution to journal › Article › peer-review

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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 language	English (US)
Pages (from-to)	41-57
Number of pages	17
Journal	Monatshefte für Mathematik
Volume	81
Issue number	1
DOIs	https://doi.org/10.1007/BF01473613
State	Published - Mar 1976

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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 Erd{\"o}s and Alaoglu on the non-existence of enumerable families of measures.",

author = "Karel Prikry",

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N2 - 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.

AB - 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.

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JO - Monatshefte für Mathematik

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

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