# A logarithmic / probabilistic version of integration.

I am searching for something of a probability analogue to integration:

$$\prod_{x_0}^{x_1} p(x)^{dx}$$

$$\int_{x_0}^{x_1} \log( p(x))dx$$
$$\exp \left( {1\over n} \sum_{k=1}^n\log(p(k))\right) = \sqrt[n]{\prod_{k=1}^{n} p(k)}$$