Fiducial inference: Difference between revisions

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Clarified the penultimate paragraph in "Background".
 
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{{unreferenced|date=July 2013}}
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In [[mathematics]], the '''Tonelli–Hobson test''' gives sufficient criteria for a function ''&fnof;'' on '''R'''<sup>2</sup> to be an [[integrable function]]. It is often used to establish that [[Fubini's theorem]] may be applied to ''&fnof;''. It is named for [[Leonida Tonelli]] and [[E. W. Hobson]].
 
More precisely, the Tonelli–Hobson test states that if ''&fnof;'' is a [[real-valued function|real-valued]] [[measurable function]] on '''R'''<sup>2</sup>, and either of the two [[iterated integral]]s
 
:<math>\int_\mathbb{R}\left(\int_\mathbb{R}|f(x,y)|\,dx\right)\, dy</math>
 
or
 
:<math>\int_\mathbb{R}\left(\int_\mathbb{R}|f(x,y)|\,dy\right)\, dx</math>
 
is finite, then ''&fnof;'' is [[Lebesgue-integrable]] on '''R'''<sup>2</sup>.
 
{{DEFAULTSORT:Tonelli-Hobson test}}
[[Category:Integral calculus]]
[[Category:Theorems in analysis]]
 
 
{{mathanalysis-stub}}

Latest revision as of 00:36, 11 August 2014

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