论文标题
图像集中的可测量动力学集合
Image sets in measurable dynamics
论文作者
论文摘要
虽然在其他动力学领域通常使用，但图像集是通常的不可脱离可测量的动力学中定义不明的对象。我们提出了一种始终如一地使用无效的图像集（尤其是量度保护）地图的图像集。这一概念在基本的千古属性的背景下进行了说明，例如复发，千古，精确性和发电机的存在。它使我们能够将有关设定理论图像的各种辅助性但从逻辑上的错误陈述转换为实际定理，并从某些经典结果中消除了图像的可测量性的额外假设。
While routinely used in other areas of dynamics, image sets are ill-defined objects in general non-invertible measurable dynamics. We propose a way of consistently working with image sets of null-preserving (and hence, in particular, of measure-preserving) maps. This concept is illustrated in the context of basic ergodic properties like recurrence, ergodicity, exactness and existence of generators. It allows us to turn various suasive but logically false statements about set-theoretic images into actual theorems, and to eliminate extra assumptions on the measurability of images from some classical results.
