Convergence of measures in forcing extensions

@article{Sobota2019ConvergenceOM,
  title={Convergence of measures in forcing extensions},
  author={Damian Sobota and Lyubomyr Zdomskyy},
  journal={Israel Journal of Mathematics},
  year={2019},
  pages={1-29}
}
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… 
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