Convergence of measures after adding a real.

Abstract

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.