  We answer the recently posed questions regarding the problem of
differentiation of integrals for the Rubio de Francia basis $\mathcal{R}$ in
the infinite torus $\mathbb{T}^\omega$. In particular, we prove that
$\mathcal{R}$ does not differentiate $L^\infty(\mathbb{T}^\omega)$. Some
remarks about differentiation in the context of arbitrary bases are also
included.
