Definition:Lebesgue Space

Definition
For $1 < p < \infty$, $\ell^p$ is the subspace of $\C^\N$ (all complex sequences) consisting of all sequences $x = \left({\mathbf{x}_n}\right)$ satisfying:
 * $\displaystyle \sum_n \left|{x_n}\right|^p < \infty$

The $L^p$ spaces are function spaces defined using natural generalizations of p-norms for finite-dimensional vector spaces.

However, according to Bourbaki's Topological Vector Spaces (1987) they were first introduced by Frigyes Riesz in 1910.