论文标题
统计空间中的加冕典礼和大块
Coronizations and big pieces in metric spaces
论文作者
论文摘要
我们证明，关于任意D期权集（不一定是图形）的加冕典礼暗示着这些（近似）集的大块。这是已知的（并且由于在足够大的共同限制的情况下，大卫和Semmes在（经典）欧几里得空间的（经典）设置中，具有Hausdorff量度的整数维度，其中近似集合的eusdorff量度为Lipschitz图。我们的结果是对这些结果的概括，我们证明加冕典礼意味着大块平方是通用属性。特别是，当适当解释的情况下，我们的结果适用于具有固定正（也许是非整数）维度的度量空间，配备了borel常规度量和任意近似集合。作为一种新颖的应用，我们强调了如何在抛物线统一的重新可相关性的背景下利用这种一般设置。
We prove that coronizations with respect to arbitrary d-regular sets (not necessarily graphs) imply big pieces squared of these (approximating) sets. This is known (and due to David and Semmes in the case of sufficiently large co-dimension, and to Azzam and Schul in general) in the (classical) setting of Euclidean spaces with Hausdorff measure of integer dimension, where the approximating sets are Lipschitz graphs. Our result is a far reaching generalization of these results and we prove that coronizations imply big pieces squared is a generic property. In particular, our result applies, when suitably interpreted, in metric spaces having a fixed positive (perhaps non-integer) dimension, equipped with a Borel regular measure and with arbitrary approximating sets. As a novel application we highlight how to utilize this general setting in the context of parabolic uniform rectifiability.
