We generalize some characterizations of uniformly rectifiable (UR) sets to sets whose Hausdorff content is lower regular (and, in particular, is not necessarily Ahlfors regular). For example, David and Semmes showed that, given an Ahlfors $d$-regular set $E$, if we consider the set $\mathcal{ℬ}$ of surface cubes (in the sense of Christ and David) near which $E$ does not look approximately like a union of planes, then $E$ is UR if and only if $\mathcal{ℬ}$ satisfies a Carleson packing condition, that is, for any surface cube $R$,

We show that, for lower content regular sets that aren’t necessarily Ahlfors regular, if ${\beta }_E\left(R\right)$ denotes the square sum of $\beta$-numbers over subcubes of $R$ as in the traveling salesman theorem for higher-dimensional sets, presented by Azzam and Schul, then

We prove similar results for other uniform rectifiability criteria, such as the local symmetry, local convexity, and generalized weak exterior convexity conditions.

En route, we show how to construct a corona decomposition of any lower content regular set by Ahlfors regular sets, similar to the classical corona decomposition of UR sets by Lipschitz graphs developed by David and Semmes.

我们将统一可校正 (Uniformly rectifiable, UR) 集的一些特征推广到其 Hausdorff 内容较低正则（特别是不一定是 Ahlfors 正则）的集。例如，David 和 Semmes 表明，给定一个 Ahlfors$d$-常规集 $乙$，如果我们考虑集合 $\mathcal{ℬ}$ 表面立方体（在基督和大卫的意义上）靠近它们 $乙$ 看起来不像平面的联合，那么 $乙$ 是 UR 当且仅当 $\mathcal{ℬ}$ 满足 Carleson 堆积条件，即对于任意曲面立方体 $\mathrm{电阻}$,

我们证明，对于不一定是 Ahlfors 正则的低内容正则集，如果 ${\beta }_{乙}\left(\mathrm{电阻}\right)$ 表示的平方和 $\beta$- 子多维数据集上的数字 $\mathrm{电阻}$ 正如 Azzam 和 Schul 提出的高维集合的旅行商定理，那么

我们证明了其他统一可纠正性标准的类似结果，例如局部对称性、局部凸性和广义弱外部凸性条件。

在此过程中，我们展示了如何构建 Ahlfors 正则集的任何低内容正则集的电晕分解，类似于 David 和 Semmes 开发的 Lipschitz 图对 UR 集的经典电晕分解。