Let G be a countable discrete group and consider a nonsingular Bernoulli shift action \( G \curvearrowright \prod _{g\in G }(\{0,1\},\mu _g)\) with two base points. We prove the first rigidity result for Bernoulli shift actions that are not measure preserving, by proving solidity for certain non-singular Bernoulli actions, making use of a new boundary associated with such Bernoulli actions. This generalizes solidity of measure preserving Bernoulli actions by Ozawa and Chifan–Ioana. For the proof, we use anti-symmetric Fock spaces and left creation operators to construct the boundary and therefore the assumption of having two base points is crucial.

设G是一个可数离散群，并考虑具有两个基点的非奇异伯努利位移动作\( G \curvearrowright \prod _{g\in G }(\{0,1\},\mu _g)\)。我们通过证明某些非奇异伯努利作用的可靠性，利用与此类伯努利作用相关联的新边界，证明了不保持测度的伯努利位移作用的第一个刚性结果。这概括了 Ozawa 和 Chifan-Ioana 保持伯努利行动的措施的可靠性。为了证明，我们使用反对称 Fock 空间和左创建算子来构造边界，因此具有两个基点的假设至关重要。