Let $X$ and $Z$ be random vectors, and $Y=g(X,Z)$. In this paper, on the one hand, for the case that $X$ and $Z$ are continuous, by using the ideas from the total variation and the flux of $g$, we develop a point of view in causal inference capable of dealing with a broad domain of causal problems. Indeed, we focus on a function, called Probabilistic Easy Variational Causal Effect (PEACE), which can measure the direct causal effect of $X$ on $Y$ with respect to continuously and interventionally changing the values of $X$ while keeping the value of $Z$ constant. PEACE is a function of $d\ge 0$, which is a degree managing the strengths of probability density values $f(x|z)$. On the other hand, we generalize the above idea for the discrete case and show its compatibility with the continuous case. Further, we investigate some properties of PEACE using measure theoretical concepts. Furthermore, we provide some identifiability criteria and several examples showing the generic capability of PEACE. We note that PEACE can deal with the causal problems for which micro-level or just macro-level changes in the value of the input variables are important. Finally, PEACE is stable under small changes in $\partial g_{in}/\partial x$ and the joint distribution of $X$ and $Z$, where $g_{in}$ is obtained from $g$ by removing all functional relationships defining $X$ and $Z$.

翻译：设 $X$ 和 $Z$ 为随机向量，且 $Y=g(X,Z)$。在本文中，一方面，针对 $X$ 和 $Z$ 为连续变量的情形，我们利用全变分与函数 $g$ 的通量思想，提出了一种能够处理广泛因果问题的因果推断视角。具体而言，我们聚焦于一个称为"概率化易变分因果效应"（PEACE）的函数，该函数可在保持 $Z$ 值不变的条件下，通过连续且干预性地改变 $X$ 的取值，度量 $X$ 对 $Y$ 的直接因果效应。PEACE 是一个关于 $d\ge 0$ 的函数，其中 $d$ 为控制概率密度值 $f(x|z)$ 强度的参数。另一方面，我们将上述思想推广至离散情形，并证明了其与连续情形的一致性。进一步地，我们利用测度论概念研究了 PEACE 的若干性质。此外，我们给出了若干可识别性准则及多个实例，以展示 PEACE 的通用能力。值得注意的是，PEACE 能够处理输入变量微观或仅宏观变化具有重要性的因果问题。最后，PEACE 对 $\partial g_{in}/\partial x$ 以及 $X$ 与 $Z$ 的联合分布的微小变化具有稳定性，其中 $g_{in}$ 是通过移除 $g$ 中定义 $X$ 和 $Z$ 的所有函数关系而得到的。