# Convergence of measures after adding a real

@inproceedings{Sobota2021ConvergenceOM, title={Convergence of measures after adding a real}, author={Damian Sobota and Lyubomyr Zdomskyy}, year={2021} }

We prove that if A is an infinite Boolean algebra in the ground model V and P is a notion of forcing adding any of the following reals: a Cohen real, an unsplit real, or a random real, then, in any P-generic extension V [G], A has neither the Nikodym property nor the Grothendieck property. A similar result is also proved for a dominating real and the Nikodym property.

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