The Ergodicity of the Convolution $μ*υ$ on a Vector Space
Yoshiaki Okazaki, Yasuji Takahashi · Publications of the Research Institute for Mathematical Sciences · 1987
Let \mathrm G be a subgroup of a vector space X and μ,υ be two probability measures on X . If μ and υ are \mathrm G -quasi-invariant and \mathrm G -ergodic, then the convolution μ*υ is also \mathrm G -ergodic.