Tonelli-Hobson test

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

More precisely, the Tonelli-Hobson test states that if "f" is a real-valued measurable function on R², and either of

:$int\_mathbb\{R\}left(int\_mathbb\{R\}|f(x,y)|dx\; ight)\; dy$

or

:$int\_mathbb\{R\}left(int\_mathbb\{R\}|f(x,y)|dy\; ight)\; dx$

exists, then "f" is Lebesgue-integrable on R².