  Sublinear expectations for uncertain processes have received a lot of
attention recently, particularly methods to extend a downward-continuous
sublinear expectation on the bounded finitary functions to one on the
non-finitary functions. In most of the approaches the domain of the extension
is not very rich because it is limited to bounded measurable functions on the
set of all paths. This contribution alleviates this problem in the
countable-state case by extending, under a mild condition, to the extended real
measurable functions on the set of c\`adl\`ag paths, and investigates when a
sublinear Markov semigroup induces a sublinear expectation that satisfies this
mild condition.
