Extend bivariate to multivariate convolution formula?

60 Views Asked by At

In reference to this post, the pdf for dependent random variables $X_1+X_2$ is given by:

$$f_{X_1+X_2}(z) = \int_{-\infty}^{\infty} f_{X_1,X_2}(x,z-x) \mathrm dx$$

How does this formula extend to the multivariate case $X_1+...+X_n$?