I recently noticed a lemma in this paper:
Wanner, Thomas. "Linearization of random dynamical systems" Dynamics reported. Springer, Berlin, Heidelberg, 1995. 203-268.
The statement in the brackets causes me confusion. Does it mean the continuity of $\nu_n(\cdot, p)$ and $\|\cdot\|_p$-convergence of $\nu_n(\cdot, p)$ imply the poinwise convergence of $\nu_n(a, p)$? This seems not quite right since norm $\|\cdot\|_p$ is not specified.
Any hint or advice would be appreciated.