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Convergence of measures in forcing extensions

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Abstract

We prove that if A is a σ-complete Boolean algebra in a model V of set theory and ℙ ∈ V is a proper forcing with the Laver property preserving the ground model reals non-meager, then every pointwise convergent sequence of measures on A is weakly convergent, i.e., A has the Vitali- Hahn-Saks property. This yields a consistent example of a whole class of infinite Boolean algebras with this property and of cardinality strictly smaller than the dominating number ∂. We also obtain a new consistent situation in which there exists an Efimov space.

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Authors and Affiliations

  1. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstraße 8-10/104, 1040, Wien, Austria

    Damian Sobota & Lyubomyr Zdomskyy

Authors
  1. Damian Sobota
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  2. Lyubomyr Zdomskyy
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Correspondence to Damian Sobota.

Additional information

The authors would like to thank the Austrian Science Fund FWF (Grant I 2374-N35) for generous support for this research.

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Sobota, D., Zdomskyy, L. Convergence of measures in forcing extensions. Isr. J. Math. 232, 501–529 (2019). https://doi.org/10.1007/s11856-019-1872-8

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  • DOI: https://doi.org/10.1007/s11856-019-1872-8

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