abelian topological (Hausdorff) semi-group （アーベル位相半群）上の確率速度についても、Choquet-Denyの定理が成り立つらしい。
Szekey, Zeng や PrunaruのA short proof of a Choquet-Deny theorem for abelian topological semigroups にある.
Theorem . Let \( (S, +) \) be an abelian topological (Hausdorff) semigroup and let \( \mu \) be a regular Borel probability measure on \( S \). Suppose that \( h : S \to \mathbb{C} \) is a bounded Borel measurable function such that
\[
h(x) = \int_S h(x + y) \, \mu(dy) \quad \text{for all} \, x \in S.
\]
Then, for each \( x \in S \), \( h(x) = h(x + y) \) for \( \mu \)-almost all \( y \in S \).