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Absolutely integrable function : ウィキペディア英語版 | Absolutely integrable function
An absolutely integrable function is a function whose absolute value is integrable, meaning that the integral of the absolute value over the whole domain is finite. For a real-valued function, since : where : this implies that both and must be finite. In Lebesgue integration, this is exactly the requirement for ''f'' itself to be considered integrable (with the integral then equaling ), so that in fact "absolutely integrable" means the same thing as "Lebesgue integrable". The same thing goes for a complex-valued function. Having a finite integral of the absolute value is equivalent to the conditions for the function to be "Lebesgue integrable". ==External links==
*(【引用サイトリンク】title=Absolutely integrable function – Encyclopedia of Mathematics )
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