# A notion of (weak) dependency

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?