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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 , although according to the Bourbaki group they were first introduced by Frigyes Riesz . 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 -norm in finite dimensions== The length of a vector in the -dimensional real vector space is usually given by the Euclidean norm: : The Euclidean distance between two points and is the length 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 -norms generalizes these two examples and has an abundance of applications in many parts of mathematics, physics, and computer science. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Lp space」の詳細全文を読む スポンサード リンク
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