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

arXiv eprints
 Pub Date:
 October 2021
 arXiv:
 arXiv:2110.04568
 Bibcode:
 2021arXiv211004568S
 Keywords:

 Mathematics  Logic;
 Mathematics  Functional Analysis;
 Mathematics  General Topology
 EPrint:
 17 pages, comments are welcome!