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

$\newcommand\v{\mathbf v}\newcommand\z{\mathbf z}\newcommand\R{\mathbb R}$This bound does not hold in such generality. E.g., suppose that $n=2$, $A=\R^2\setminus\{(0,0)\}$, $P(\v=(0,0))=1$, $P(\z=(1,0)...
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