论文标题
稳定性，角落和其他二维形状
Stability, corners, and other 2-dimensional shapes
论文作者
论文摘要
我们引入了一种称为稳定稳定性的稳定性的放松，这对loeb量的子集对伪芬属组的扰动不敏感。我们表明，稳健的稳定性满足了测量独立元素的平稳性原理。我们应用这一原理来推断非标准有限群（可能是非阿布莱安人）的笛卡尔产品的密集稳定稳定子集中的正方形的存在。我们的结果意味着有限群体的笛卡尔产品定性渐近版本。在最后一部分中，我们建立了$ 3 \ times 2 $ - 格里德斯（以及$ l $ - 形状）的密集稳定稳定的$ 2 $ 2 $ 2 $维的子集的有限亚伯利亚奇数订单的子集。
We introduce a relaxation of stability, called robust stability, which is insensitive to perturbations by subsets of Loeb measure $0$ in a pseudofinite group. We show that robust stability satisfies a stationarity principle for measure independent elements. We apply this principle to deduce the existence of squares in dense robustly stable subsets of Cartesian products of non-standard finite groups, possibly non-abelian. Our results imply qualitative asymptotic versions for Cartesian products of finite groups. In the final section, we establish the existence of $3\times 2$-grids (and thus of $L$-shapes) in dense robustly stable $2$-dimensional subsets of finite abelian groups of odd order.
