1.6. Let f be a real bounded continuous function on :li1 and J-t a p.m. on

}')l1 such that V'x E gel: f(x) = r f(x + y)J-t(dy). )9{1 Then f (x + s) = f (x) for each s in the support of J-t. In particular, if J-t is not of the lattice type, then f is constant everywhere. [This is due to G. A. Hunt, who used it to prove renewal limit theorems. The approach was later rediscovered by other authors, and the above result in somewhat more general context is now referred to as Choquet-Deny's theorem.]