发表机构
Sun Yat-sen University（中山大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用完备根视图研究局部紧sofic群泊松作用的测度sofic熵，证明非紧局部紧第二可数sofic群的正强度泊松作用具完全正测度sofic熵，还比较了相关熵公式并指出非紧性是定理成立的必要条件。
AI 中文摘要
本文利用完备根视图研究局部紧sofic群的泊松作用的测度sofic熵。我们证明，对每个非紧、局部紧、第二可数的sofic群及每个局部紧sofic逼近，每个正强度的泊松作用都具有完全正的测度sofic熵。我们还将平均空间公式和逐点空间公式与Singh熵进行比较，并表明对于所述定理，非紧性是必要条件。
英文摘要
We prove that every Poisson action of positive intensity of a noncompact locally compact second countable sofic group has completely positive measure sofic entropy with respect to every locally compact sofic approximation. The proof constructs random microstates for arbitrary measurable factors by completing local Poisson configurations with an independent exterior Poisson process. Probability estimates and a packing argument then show that every nontrivial factor has positive entropy. We also give a compact-group example showing that the noncompactness assumption is essential.
