  We consider the joint lower expectation of a finite-state imprecise
stochastic process, defined using either the Ville-Vovk-Shafer natural
extension or the Williams natural extension. In both cases, we show that it is
continuous with respect to the pointwise convergence of non-decreasing
sequences of real-valued functions $f_n$, $n\in\mathbb{N}_0$, where each $f_n$
is $n$-measurable. For the Ville-Vovk-Shafer natural extension, a similar
result is shown to hold for non-increasing sequences, provided that they
converge to a bounded function.
