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| In ], a ] or ]-valued function of a real variable is '''square-integrable''' on an interval if the integral over that interval of the square of its absolute value is finite. The set of all ]s that are square-integrable forms a ], the so-called ] | In ], a ] or ]-valued function of a real variable is '''square-integrable''' on an interval if the integral over that interval of the square of its absolute value is finite. The set of all ]s that are square-integrable forms a ], the so-called ] | ||
Revision as of 15:10, 7 January 2004
In mathematical analysis, a real- or complex-valued function of a real variable is square-integrable on an interval if the integral over that interval of the square of its absolute value is finite. The set of all measurable functions that are square-integrable forms a Hilbert space, the so-called Lp space