Theorem Statement
Suppose A and B are complete measure spaces. Suppose f(x,y) is A × B measurable. If
where the integral is taken with respect to a product measure on the space over A × B, then
the first two integrals being iterated integrals with respect to two measures, respectively, and the third being an integral with respect to a product of these two measures.
If the above integral of the absolute value is not finite, then the two iterated integrals may actually have different values. See below for an illustration of this possibility.
Read more about this topic: Fubini's Theorem
Famous quotes containing the words theorem and/or statement:
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)
“No statement about God is simply, literally true. God is far more than can be measured, described, defined in ordinary language, or pinned down to any particular happening.”
—David Jenkins (b. 1925)