L2 space

The $L^2$ space consists of all measurable functions for which the square of the absolute value is Lebesgue integrable. Formally, a function $f$ belongs to the $L^2$ space on a measure space $(\Omega ,\mathcal{F},\mu )$ if:

$${\int }_{\Omega }|f(x){|}^{2}d\mu (x)<\infty$$

In simpler terms, $f$ is square-integrable if the integral of $|f(x){|}^2$ over the domain $\Omega$ is finite.