Products of random varibles depending on a random walk

LetX=(X_n)_n0 denote an irreducible random walk (ergodic in the sense of [7]) on a compact metrizable abelian groupG. In this paper we characterize completely the limit distributions of the productsY_n=X₀...X_n. In particular we find necessary and sufficient conditions forX and/orG to imply that the products are asymptotically equidistributed in the mean, i. e. {im171-1} holds for all open,m_G-regular subsetsA ofG (m_G: normalized Haar measure).—For example ifG is monothetic and connected or ifX is asymptotically equidistributed (not merely in the mean) then the products are asymptotically equidistributed in the mean.Dedicated to Prof. Dr. L. Schmetterer on his 60^th Birthday