## 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 language | English (US) |
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Pages (from-to) | 105-112 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 80 |

Issue number | 1 |

DOIs | |

State | Published - 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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