Lp space

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In mathematics, the Lp spaces are function spaces defined using natural generalizations of p-norms for finite-dimensional vector spaces. They are sometimes called Lebesgue spaces, named after Henri Lebesgue (Dunford & Schwartz 1958, III.3), although according to Bourbaki (1987) they were first introduced by Riesz (1910). They form an important class of examples of Banach spaces in functional analysis, and of topological vector spaces. Lebesgue spaces have applications in physics, statistics, finance, engineering, and other disciplines.

Contents

Motivation

Consider the real vector space Rn. The sum of two vectors in Rn is given by

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