Upper Banach density
= Upper Banach density
{title2=$d^*(S)$}
{wiki}
For $S\subseteq\mathbb Z$, its upper Banach density is
$$
d^*(S)=\limsup_{N\to\infty}\sup_{m\in\mathbb Z}\frac{|S\cap[m,m+N-1]|}{N}.
$$
= Upper Banach density
{title2=$d^*(S)$}
{wiki}
For $S\subseteq\mathbb Z$, its upper Banach density is
$$
d^*(S)=\limsup_{N\to\infty}\sup_{m\in\mathbb Z}\frac{|S\cap[m,m+N-1]|}{N}.
$$