A Boolean Lévy group with a free nonsingular action
We construct a Boolean Lévy group with a free ergodic spatial nonsingular action on a standard probability space, answering a question of Glasner, Tsirelson and Weiss. The action admits no equivalent invariant $\sigma$-finite measure. The group is a quotient of a weighted summable Boolean group by a discrete subgroup. By the nonsingular fixed-point theorem of Avraham-Re'em and Peterzil, the resulting group is not locally Wasserstein.
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