On the residuality of mixing by convolutions probabilities

A probability measureμ on a locally compactσ — compact amenable Hausdorff groupG is called mixing by convolutions if for every pair of probabilitiesν ₁,ν ₂ onG we have: $$mathop {lim }limits_{n to infty } left| {left( {nu _1 - nu _2 } right) star mu ^{ star n} } right| = mathop {lim }limits_{n to infty } left| {left( {nu _1 - nu _2 } right) star mu ^{ star n} } right| = 0.$$ . It is proved that the set of all mixing by convolutions probabilities is a norm (variation) dense subset of the setP(G) of all probabilities onG. IfG is additionally second countable the mixing measures are residual inP(G).