1
vote
0answers
32 views

Recurrence for upper Banach Density

Let $E\subseteq \mathbb{Z}$ have $d^*(E) >0$ where $d^*$ is upper Banach density. I am trying to understand why there must exist an $1\leq n \leq \frac{1}{d^*(E)} + 1$ such that $d^*(E\cap (E-n)) ...
3
votes
0answers
120 views

The measures in Furstenberg's correspondence

In the paper Inverting the Furstenberg correspondence (IFC), the author defines a function $D_{A}(\sigma)$ on the Basic clopens of Cantor space, $2^{\mathbb{N}}$, where $A$ is a finite binary string ...