论文标题
不包含给定无限序列的副本的大型集
Large sets containing no copies of a given infinite sequence
论文作者
论文摘要
假设$ a_n $是一个真实的非负序列，不会呈指数级增加。对于任何$ p <1 $，我们都会征收Lebesgue可测量的$ e \ subseteq \ mathbb {r} $，该$在任何单位间隔中至少都测量了$ p $，并且不包含affine coppy $ \ {x+ta_n：\ n \ in \ mathbb {n} \ n} $ x $ x \ in v in \ mathbb {n} 0 $）。我们将其推广到更高的维度，也将其概括为序列的一些``非线性''副本。我们的方法是概率。
Suppose $a_n$ is a real, nonnegative sequence that does not increase exponentially. For any $p<1$ we contruct a Lebesgue measurable set $E \subseteq \mathbb{R}$ which has measure at least $p$ in any unit interval and which contains no affine copy $\{x+ta_n:\ n\in\mathbb{N}\}$ of the given sequence (for any $x \in \mathbb{R}, t > 0$). We generalize this to higher dimensions and also for some ``non-linear'' copies of the sequence. Our method is probabilistic.
