k-finiteness and k-additivity of measures on sets and left invariant measures on discrete groups

Thomas E. Armstrong, Karel Prikry

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

For any cardinal k a possibly infinite measure μ > 0 on a set X is strongly nonadditive if X is partitioned into k or fewer ii-negligible sets. The measure μ is purely non-K-additive if it dominates no nontrivial K-additive measure. The properties and relationships of these types of measures are examined in relationship to measurable ideal cardinals and real-valued measurable cardinals. Any K-finite left invariant measure μ on a group G of cardinality larger than k is strongly non-K-additive. In particular, σ-finite left invariant measures on infinite groups are strongly finitely additive.

Original languageEnglish (US)
Pages (from-to)105-112
Number of pages8
JournalProceedings of the American Mathematical Society
Volume80
Issue number1
DOIs
StatePublished - Sep 1980

Keywords

  • Ic-finiteness
  • K-additivity
  • K-complete ideal
  • Left invariant means
  • Left invariant measures
  • Pure non-K-additivity
  • Real-valued measurable cardinal
  • «-saturated ideal

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