In mathematics, a square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function,[1] is a real- or complex-valued measurable function for which the integral of the square of the absolute value is finite. Thus, square-integrability on the real line ( − ∞ , + ∞ ) {\displaystyle (-\infty ,+\infty )} is defined as follows.