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首页> 外文期刊>Journal d'analyse mathematique >ON SIMPLICITY CONCEPTS FOR ERGODIC ACTIONS
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ON SIMPLICITY CONCEPTS FOR ERGODIC ACTIONS

机译：关于人体动作的简单概念

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A weakly mixing measure preserving action of a locally compact second countable group on a standard probability space is called 2-fold near simple if every ergodic joining of it with itself is either product measure or is supported on a ‘convex combination’ of graphs. A similar definition can be given for near simplicity of higher order. This generalizes the Veech–del Junco–Rudolph notion of simplicity. Our main results include the following. An analogue of Veech theorem on factors holds for the 2-fold near simple actions. A weakly mixing group extension of an action with near MSJ is near simple. The action of a normal co-compact subgroup is near simple if and only if the whole action is near simple. The subset of all 2-fold near simple transformations (i.e., Z-actions) is meager in the group of measure preserving transformations endowed with the weak topology. Via the (C, F)-construction, we produce a near simple quasi-simple transformation which is disjoint from any simple map.
机译：如果局部紧凑的第二个可数组在标准概率空间上的弱混合度量保持作用被称为2倍近似简单，如果它的每次遍历连接本身都是乘积度量或在图的“凸组合”上得到支持。可以给出相似的定义，以使高阶几乎简单。这概括了Veech–del Junco–Rudolph的简单性概念。我们的主要结果如下。 Veech定理的因子类似物可将简单动作保留2倍。一个动作与近MSJ的弱混合群扩展几乎是简单的。当且仅当整个动作接近简单时，正常的同伴亚组的动作才接近简单。在具有弱拓扑的保留度量的变换组中，所有2折近的简单变换（即Z动作）的子集很少。通过（C，F）构造，我们生成了几乎简单的准简单变换，该变换与任何简单映射都不相交。

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