Ordered groups | Functional analysis

Riesz space

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. For example, 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. (Wikipedia).

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Related pages

Mathematical economics | Order complete | Order unit | Freudenthal spectral theorem | Topological homomorphism | Frigyes Riesz | Almost everywhere | Lattice (order) | Archimedean property | Topological vector lattice | Absorbing set | Order dual (functional analysis) | Order bound dual | Quotient space (linear algebra) | Band (order theory) | Distributive lattice | Injective function | Approximately finite-dimensional C*-algebra | Homogeneous function | Regular category | Pointwise | Preorder | Cardinal number | Mathematics | Solid set | Real number | Cone-saturated | Order topology (functional analysis) | Ordered vector space | Polar set | Zeros and poles | Partially ordered space | Direct sum | Balanced set | Archimedean ordered vector space | Lp space | Boolean algebra | Charalambos D. Aliprantis | Radon–Nikodym theorem | Convex set | Order isomorphism