What is "superficial density" in the context of integration (over surfaces)? I have read something like this: > We have $$\int_{M}f(x)d\sigma(x) = 1$$ where $d\sigma$ is the superficial density. What does this mean?...--prophetes.ai

What is "superficial density" in the context of integration (over surfaces)? I have read something like this: > We have $$\int_{M}f(x)d\sigma(x) = 1$$ where $d\sigma$ is the superficial density. What does this mean? $M$ is a hypersurface/manifold. The author does not define it.

Wikipedia article Area density begins with

> The area density (also known as areal density, surface density, or superficial density) ...

In mathematics, it is more common to call this "surface measure".