Tonelli-Hobson test

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.


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