论文标题
通过瓷砖和统一的联合标记的比例千古定理
A ratio ergodic theorem via tiling and uniformly syndetic markers
论文作者
论文摘要
我们证明了道克（Dowker）比率ergodic定理的纯bor/无测量版本，从中，我们从中得出了对道克（Dowker）原始定理的加强，并确切地识别了局部ergodic比率的极限。这是通过在更复杂的连续体转换中实现[TSE18]的刻板瓷砖思想来完成的。在此过程中，我们为这些转变建立了消失的标记引理，该引理概括了其众所周知的可逆转换。
We prove a purely Borel/measureless version of Dowker's ratio ergodic theorem, from which we derive a strengthening of Dowker's original theorem with a precise identification of the limit of local ergodic ratios. This is done by implementing the pointwise tiling idea of [Tse18] in the more complex setting of continuum-to-one Borel transformations. Along the way, we establish a vanishing markers lemma for these transformations, which generalizes its well-known counterpart for invertible transformations.
