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)
“He that writes to himself writes to an eternal public. That statement only is fit to be made public, which you have come at in attempting to satisfy your own curiosity.”
—Ralph Waldo Emerson (1803–1882)