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In mathematics, a Riesz space, lattice-ordered vector space or vector lattice is a partially ordered vector space where the order structure is a lattice. Riesz spaces are named after Frigyes Riesz who first defined them in his 1928 paper ''Sur la décomposition des opérations fonctionelles linéaires''. Riesz spaces have wide ranging applications. They are important in measure theory, in that important results are special cases of results for Riesz Spaces. E.g. the Radon–Nikodym theorem follows as a special case of the Freudenthal spectral theorem. Riesz spaces have also seen application in Mathematical economics through the work of Greek-American economist and mathematician Charalambos D. Aliprantis. == Definition == A Riesz space is defined to be a vector space endowed with a partial order, , that for any in , satisfies: # Translation Invariance: implies . # Positive Homogeneity: For any scalar , implies . # For any pair of vectors in there exists a supremum (denoted ) in with respect to the partial order of the lattice structure . 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「Riesz space」の詳細全文を読む スポンサード リンク
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