Quasifactors of Ergodic Systems with Positive Entropy

The relation between the two notions quasifactors and joinings is investigated and the notion of a joining quasifactor is introduced. We clarify the close connection between quasifactors and symmetric infinite selfjoinings which arises from de Finetti-Hewitt-Savage theorem. Unlike the zero entropy case where quasifactors seems to preserve some properties of their parent system, it is shown that any ergodic system of positive entropy admits all ergodic systems of positive entropy as quasifactors. A restricted version of this result is obtained for joining quasifactors. §0. Introduction For a measure preserving transformation (X,X , μ, T ), a factor system (Y,Y, ν, S) with a factor map π : X → Y , can be viewed as the T -invariant subalgebra π−1(Y) ⊂ X . One can also describe the factor (Y,Y, ν, S) as a measure preserving transformation on the space M(X) of probability measures on X as follows. Disintegrate the measure μ along the fibers of π−1(Y),