• Corpus ID: 125511993

Measurability Properties on Small Cardinals

  title={Measurability Properties on Small Cardinals},
  author={Monroe Eskew},
Author(s): Eskew, Monroe Blake | Advisor(s): Zeman, Martin | Abstract: Ulam proved that there cannot exist a probability measure on the reals for which every set is measurable and gets either measure zero or one. He asked how large a collection of partial 0-1 valued measures is required so that every set of reals is measurable in one of them. Alaoglu and Erdos proved that if the continuum hypothesis holds, then countably many measures is not enough, and Ulam asked if aleph_1 many can suffice… 

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