We prove that if $\mathcal{ A}$ is a $\sigma$-complete Boolean algebra in a model $V$ of set theory and $\mathbb{ P}\in V$ is a proper forcing with the Laver property preserving the ground model reals non-meager, then every pointwise convergent sequence of measures on $\mathcal{ A}$ in a $\mathbb{ P}$-generic extension $V[G]$ is weakly convergent, i.e. $\mathcal{ A}$ has the Vitali--Hahn--Saks property in $V[G]$. 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 $\mathfrak{ d}$. We also obtain a new consistent situation in which there exists an Efimov space.
Categories: math.FA math.LO