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... > algebra > linear algebra > vector space > topological vector space > normed vector space > Banach space > Lp space
mathematical analysis > functional analysis > function space > Lp space
set theory > function space > Lp space
algebra > linear algebra > function space > Lp space
category theory > function space > Lp space
probability theory > measure theory > Lp space

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Lp space  

Definition

  • In mathematics, the Lp spaces are function spaces defined using a natural generalization of the p-norm for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to the Bourbaki group (Bourbaki 1987) they were first introduced by Frigyes Riesz (Riesz 1910).
    Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. 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.
    (Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Lp_space)

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