Lp space

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the Lp spaces are <a href="/facts/Function_space/lLUE2R1t">function spaces</a> defined using a natural generalization of the <a href="/facts/Norm_(mathematics)/xIbR4uE1">p-norm</a> for finite-dimensional <a href="/facts/Vector_space/M1pxMLx2">vector spaces</a>. They are sometimes called Lebesgue spaces, named after <a href="/facts/Henri_Lebesgue/ysngVGXc">Henri Lebesgue</a> (Dunford & Schwartz 1958, III.3), although according to the <a href="/facts/Nicolas_Bourbaki/qRJhs9nr">Bourbaki</a> group (Bourbaki 1987) they were first introduced by <a href="/facts/Frigyes_Riesz/EN47QveQ">Frigyes Riesz</a> (Riesz 1910). 
Lp spaces form an important class of <a href="/facts/Banach_space/sDEIk7EC">Banach spaces</a> in <a href="/facts/Functional_analysis/MIp233MT">functional analysis</a>, and of <a href="/facts/Topological_vector_space/XRex1ChN">topological vector spaces</a>. 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.

Lp space open-in-new

Lp space