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In page Ergodic flow:
"In the dissipative case, A = L∞(R) with R acting by translation, which is just the induced action from the ergodic translation action of Z on (Z), corresponding to the atomic measure space Z with the discrete measure. So it can be assumed that the flow is properly ergodic. In particular for any p ≠ 0, 1 in A there is a T > 0 without σT(p) ≤ p, so that (1 − p) ∧ σT(p) ≠ 0. On the other hand as r > 0 decreases to zero
