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In mathematical analysis Fubini's theorem, introduced by , is a result which gives conditions under which it is possible to compute a double integral using iterated integrals. One may switch the order of integration if the double integral yields a finite answer when the integrand is replaced by its absolute value. : As a consequence it allows the order of integration to be changed in iterated integrals. Fubini's theorem implies that the two repeated integrals of a function of two variables are equal if the function is integrable. Tonelli's theorem introduced by is similar but applies to functions that are non-negative rather than integrable. ==History== The special case of Fubini's theorem for continuous functions on a product of closed bounded subsets of real vector spaces was known to Euler in the 18th century. extended this to bounded measurable functions on a product of intervals. conjectured that the theorem could be extended to functions that were integrable rather than bounded, and this was proved by . gave a variation of Fubini's theorem that applies to non-negative functions rather than integrable functions. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Fubini's theorem」の詳細全文を読む スポンサード リンク
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