Under suitable integrability conditions, the integral of a function of two variables over a product space can be computed as an iterated integral, in either order. Named for Guido Fubini, it is a basic tool for evaluating multi-dimensional integrals.
Facts
StatementFubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, integrating one variable at a time. 1 Classification
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Source Fubini's Theorem (Wikipedia)
Sources
1. Fubini's Theorem (Wikipedia)
Wikimedia FoundationLead section, opening sentence
Fubini's theorem gives the conditions under which a double integral can be computed as an iterated integral, i.e. by integrating in one variable at a time.
History section
this was proven by Fubini in 1907.
Proved By: Guido Fubini, Lead
The theorem is named after Guido Fubini, who proved a general result in 1907; special cases were known earlier through results such as Cavalieri's principle, which was used by Leonhard Euler.
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