Lebesgue Integrable Function

a function to which the concept of the integral introduced by W. Lebesgue may be applied. In other words, an integrable function is a function whose Lebesgue integral, taken over a given set, is finite. The function must be Lebesgue measurable. Lebesgue integrable functions are often referred to simply as integrable functions. A square integrable function is a measurable function whose square is an integrable function.