Riesz decomposition property
The (partially) ordered vector space has the Riesz decomposition property if for all , or, equivalently, if for all , .
The Riesz decomposition property and the Riesz decomposition theorem are quite different (although there is a link) and, in fact, the property does turn up as an axiom used in axiomatic potential theory (see also Potential theory, abstract), see [a1], where it is called the axiom of natural decomposition.
|[a1]||C. Constantinescu, A. Cornea, "Potential theory on harmonic spaces" , Springer (1972) pp. 104|
|[a2]||W.A.J. Luxemburg, A.C. Zaanen, "Riesz spaces" , I , North-Holland (1971) pp. 73|
|[a3]||P. Meyer-Nieberg, "Banach lattices" , Springer (1971) pp. 3, Thm. 1.1.1|
|[a4]||G.K. Pedersen, "-algebras and their automorphism groups" , Acad. Press (1979) pp. 14|
|[a5]||Y.-Ch. Wong, K.-F. Ng, "Partially ordered topological vector spaces" , Oxford Univ. Press (1973) pp. 9|
Riesz decomposition property. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Riesz_decomposition_property&oldid=18014