  We consider discrete-time uncertain processes with finite state space and
study the properties of game-theoretic upper expectations developed by Shafer
and Vovk. We start by proving some basic properties, e.g. monotonicity, law of
iterated upper expectations,... Afterwards, we show that this operator
satisfies several, more involved continuity properties, including continuity
with respect to non-decreasing sequences and continuity with respect to
specific sequences of so-called `finitary measurable' functions, which are
functions that depend on a finite number of states.
