On the K property for Maharam extensions of Bernoulli shifts and a question of Krengel

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We show that the Maharam extension of a conservative. non singular K Bernoulli shift without an a.c.i.p. 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 IIIλwith λnot equal to 1 Bernoulli shift. A conservative non singular K Bernoulli shift is either of type II₁ or of type III₁.