Common
Square-integrable function
Function whose squared absolute value has finite integral
Square-integrable function
In mathematics, a square-integrable function, also called a quadratically integrable function or L 2 {\displaystyle L^{2}} function or square-summable function, 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. One may also speak of quadratic integrability over bounded intervals such as [ a , b ] {\displaystyle [a,b]} for a ≤ b {\displaystyle a\leq b} . An equivalent definition is to say that the square of the function itself (rather than of its absolute value) is Lebesgue integrable...
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