Is there a name for the integral used to define square integrable functions?

Question

A square integrable function on $\mathbb{R}^n$ would be defined as a function $f(\mathbf{x})$ satisfying the constraint $$ \int |f(\mathbf{x})|^2 d^n\mathbf{x} < \infty, $$ for $\mathbf{x} \in \mathbb{R}^n$. Is there a specific name given to the quantity $$ \int |f(\mathbf{x})|^2 d^n\mathbf{x}? $$

Answer 1

This is the square of a quantity normally called the $2$-norm, or the $L^2$-norm. As its name suggests, it is a norm on the space of square-integrable functions, which is called $L^2(\mathbb{R}^n)$.