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Difference of probabilities of two random vectors lying in the same set

Suppose I have to random vectors: $$\mathbf{z} = (z_1, \dots, z_n)^T, \quad \mathbf{v} = (v_1, \dots, v_n)^T$$ and set $A \subset \mathbb{R}^n$. I want to find an upper bound $B$ for the following dif …