Multivariate Real Densities

Definition

A multivariate density or joint density is a function from $n$-dimensional real space to the real numbers which is nonnegative and and normalized. A real-valued function on $n$-dimensional real space is normalized if it integrates to 1.

Notation

$f: \R ^d \to \R $ with $f \geq 0$ and $\int f = 1$ is a density.