A Note on Cocycles of Unitary Representations

Given a unitary representation of a locally compact abelian group , we investigate the relationship between two cocycles <!-- MATH ${a_1},{a_2}:V{a_1} = {a_2} + b$ --> for some unitary operator commuting with and some coboundary . A necessary and sufficient condition is given in terms of canonical-finite measures defined on . These results are applied to the representation of defined by the shift of a stationary Markov chain.