Tonelli–Hobson test

From Wikipedia, the free encyclopedia
Jump to: navigation, search

In mathematics, the Tonelli–Hobson test gives sufficient criteria for a function ƒ on R2 to be an integrable function. It is often used to establish that Fubini's theorem may be applied to ƒ. It is named for Leonida Tonelli and E. W. Hobson.

More precisely, the Tonelli–Hobson test states that if ƒ is a real-valued measurable function on R2, and either of the two iterated integrals


is finite, then ƒ is Lebesgue-integrable on R2.