Tonelli-Hobson test

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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\right) dy

or

\int_\mathbb{R}\left(\int_\mathbb{R}|f(x,y)|dy\right) dx

exists, then f is Lebesgue-integrable on R2.

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