New answers tagged privacy
1
If you are working with discrete probability distributions, then for any subset $S$ of the range, you have
$$
\Pr[\mathcal{M}(x)\in S]
= \sum_{s\in S} \Pr[\mathcal{M}(x)=s]
\leq \sum_{s\in S} e^\varepsilon \Pr[\mathcal{M}(x')=s]
= e^\varepsilon \Pr[\mathcal{M}(x')\in S]
$$
and so the second definition implies the first (and thus they are equivalent).
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