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In mathematics, the 'Tonelli-Hobson test' gives sufficient criteria for a function ''f'' on 'R'² 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 'R'², 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 'R'².