Pointwise maximal leakage (PML) is an operationally meaningful privacy measure that quantifies the amount of information leaking about a secret $X$ to a single outcome of a related random variable $Y$. In this paper, we extend the notion of PML to random variables on arbitrary probability spaces. We develop two new definitions: First, we extend PML to countably infinite random variables by considering adversaries who aim to guess the value of discrete (finite or countably infinite) functions of $X$. Then, we consider adversaries who construct estimates of $X$ that maximize the expected value of their corresponding gain functions. We use this latter setup to introduce a highly versatile form of PML that captures many scenarios of practical interest whose definition requires no assumptions about the underlying probability spaces.

翻译：点态最大泄露（PML）是一种具有操作意义的隐私度量，用于量化关于秘密变量$X$的信息通过相关随机变量$Y$的单个结果泄露的量。本文中，我们将PML的概念扩展到任意概率空间上的随机变量。我们提出了两种新定义：首先，通过考虑试图猜测$X$的离散（有限或可数无穷）函数值的对手，将PML推广到可数无穷随机变量；其次，我们考虑构造$X$的估计以最大化其相应增益函数期望值的对手。基于后一种设置，我们引入了一种高度通用的PML形式，该形式涵盖了多种实际场景，且其定义无需对底层概率空间做任何假设。