BERNOULLI ACTIONS OF TYPE III WITH PRESCRIBED ASSOCIATED FLOW

Abstract We prove that many, but not all, injective factors arise as crossed products by nonsingular Bernoulli actions of the group $\mathbb {Z}$ . obtain this result proving a completely general on ergodicity, type and Krieger’s associated flow for shifts with arbitrary base spaces. must satisfy structural property infinite divisibility. Conversely, we all almost periodic flows, well many other ergodic do weakly mixing action any amenable group. As byproduct, weights are tensor $2 \times 2$ matrices. Finally, construct Poisson suspension prescribed locally compact second countable does have (T).