Let $\nu$ be a probability measure over some product metric space $\mathcal{X}^n$ such that there exist some $\alpha \geq 0$ for which for every $1\leq i \leq n$ it holds that
$\sup_{x\in \mathcal{X}^n} ||\nu_i - \nu_i (\cdot | x^{-i})||_{TV} \leq \alpha$.
The definition can be regarded as some kind of dependency bound (parameterized by $\alpha$).
Is it known? does it have a name? If not, is there any closely related notion of dependency?
