We study the independence density for finite families of finite tuples of sets for continuous actions of discrete groups on compact metrizable spaces. We use it to show that actions with positive naive entropy are Li–Yorke chaotic and untame. In particular, distal actions have zero naive entropy. This answers a question of Lewis Bowen.

中文翻译：

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组合独立性和朴素熵

我们研究了离散群在紧凑可度量空间上的连续动作的有限元组集合的有限族的独立密度。我们用它来表明具有正朴素熵的动作是 Li-Yorke 混乱和不驯服的。特别是，远端动作的初始熵为零。这回答了刘易斯鲍文的一个问题。