In
mathematics, a square-integrable function, also called a quadratically integrable function or
function or square-summable function,
is a
real- or
complex-valued
measurable function
In mathematics and in particular measure theory, a measurable function is a function between the underlying sets of two measurable spaces that preserves the structure of the spaces: the preimage of any measurable set is measurable. This is i ...
for which the
integral
In mathematics, an integral assigns numbers to functions in a way that describes displacement, area, volume, and other concepts that arise by combining infinitesimal data. The process of finding integrals is called integration. Along with ...
of the square of the
absolute value is finite. Thus, square-integrability on the real line
is defined as follows.
One may also speak of quadratic integrability over bounded intervals such as