LP

LP or lp may stand for:

Music

Companies and organizations

Lp space

In mathematics, the L^p 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). L^p 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.

The p-norm in finite dimensions

The length of a vector x = (x₁, x₂, ..., x_n) in the n-dimensional real vector space Rⁿ is usually given by the Euclidean norm:

The Euclidean distance between two points x and y is the length ||x − y||₂ of the straight line between the two points. In many situations, the Euclidean distance is insufficient for capturing the actual distances in a given space. An analogy to this can be found in Manhattan taxi drivers who should measure distance not in terms of the length of the straight line to their destination, but in terms of the Manhattan distance, which takes into account that streets are either orthogonal or parallel to each other. The class of p-norms generalizes these two examples and has an abundance of applications in many parts of mathematics, physics, and computer science.

L&P

L&P may refer to: