Li-Feng Xi

The Erd\H{o}s similarity problem for null sequences with adjacent ratios bounded below

Let $(a_n)$ be a positive null sequence with $\liminf_{n\to\infty}a_{n+1}/a_n>0$. For every $\eta>0$, we construct a compact set $E\subset[0,1]$ with Lebesgue measure greater than $1-\eta$ containing no nontrivial affine copy of $\{a_n:n\ge1\}$. No monotonicity is assumed. The proof adapts a finite-tree construction fo...