We show that the Maharam extension of a type III, conservative and nonsingular K Bernoulli is a K-transformation. This together with the fact that the Maharam extension of a conservative transformation is conservative gives a negative answer to Krengel’s and Weiss’s questions about existence of a type II∞ or type IIIλ with λ ≠ 1 Bernoulli shift. A conservative non-singular K, in the sense of Silva and Thieullen, Bernoulli shift is either of type II1 or of type III1.
Bibliographical noteFunding Information:
∗This research was was supported by The Israel Science Foundation grant No. 1114/08. Received May 9, 2012 and in revised form October 31, 2012
© 2014, Hebrew University Magnes Press.