A remark on the ultrapower algebra of the hyperfinite factor

On page 43 in \cite{Po83} Sorin Popa asked whether the following property holds: \emph{If $\omega$ is a free ultrafilter on $\mathbb{N}$ and $\mathcal R_1\subseteq \mathcal R$isanirreducibleinclusionofhyperfiniteII$_1$factorssuchthat$\mathcal R’\cap \mathcal R^\omega\subseteq \mathcal R^\omega_1$doesitfollowsthat$\mathcal R_1=\mathcal R$?} In this short note we provide an affirmative answer to this question.