Riesz space

In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a Riesz space, lattice-ordered vector space or vector lattice is a <a href="/facts/Ordered_vector_space/yN9VfKMa">partially ordered vector space</a> where the <a href="/facts/Order_structure/gn6fM3oJ">order structure</a> is a <a href="/facts/Lattice_(order)/5ak6ufky">lattice</a>.
Riesz spaces are named after <a href="/facts/Frigyes_Riesz/EN47QveQ">Frigyes Riesz</a> 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 <a href="/facts/Measure_theory/yCq7zlI4">measure theory</a>, in that important results are special cases of results for Riesz spaces. For example, the <a href="/facts/Radon%E2%80%93Nikodym_theorem/uWepNG2B">Radon–Nikodym theorem</a> follows as a special case of the <a href="/facts/Freudenthal_spectral_theorem/t9oFUqsN">Freudenthal spectral theorem</a>. Riesz spaces have also seen application in <a href="/facts/Mathematical_economics/Dvy7j519">mathematical economics</a> through the work of Greek-American economist and mathematician <a href="/facts/Charalambos_D._Aliprantis/7XDqkxk3">Charalambos D. Aliprantis</a>.

Riesz space open-in-new

Riesz space