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Lp space
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{{DISPLAYTITLE:''L''<sup>''p''</sup> space}} {{Short description|Function spaces generalizing finite-dimensional p norm spaces}} In [[mathematics]], the '''{{math|''L''<sup>''p''</sup>}} spaces''' are [[function space]]s defined using a natural generalization of the [[Norm (mathematics)#p-norm|{{math|''p''}}-norm]] for finite-dimensional [[vector space]]s. They are sometimes called '''Lebesgue spaces''', named after [[Henri Lebesgue]] {{harv|Dunford|Schwartz|1958|loc=III.3}}, although according to the [[Nicolas Bourbaki|Bourbaki]] group {{harv|Bourbaki|1987}} they were first introduced by [[Frigyes Riesz]] {{harv|Riesz|1910}}. {{math|''L''<sup>''p''</sup>}} spaces form an important class of [[Banach space]]s in [[functional analysis]], and of [[topological vector space]]s. Because of their key role in the mathematical analysis of measure and probability spaces, Lebesgue spaces are used also in the theoretical discussion of problems in physics, statistics, economics, finance, engineering, and other disciplines.
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