Riesz space

Summary

A Riesz space, or vector lattice, is an ordered vector space whose order is a lattice. It is at the same time a real vector space and a lattice-ordered group. Spaces of real functions with the pointwise order, such as spaces of continuous functions and $L^p$ spaces, are Riesz spaces. Riesz spaces are the setting for positive operators and for Banach lattices in functional analysis.