L^p Space

L^p Space

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 Bourbaki (1987) they were first introduced by Riesz (1910). Lp spaces form an important class of Banach spaces in functional analysis, and of topological vector spaces. Lebesgue spaces have applications in physics, statistics, finance, engineering, and other disciplines.