Riesz Spaces

Abstract

We assume the reader to be familiar with the basic definitions and simplest properties of real and complex vector spaces. In the present section and the next ones we restrict ourselves to real vector spaces. Elements in the vector spaces will usually be denoted by f, g, h,… and the real numbers which act as scalar multipliers by α, β,… (this choice for the notation is related to the fact that in many examples the space consists of realvalued functions). The null element (zero element, neutral element) with respect to addition will be denoted by 0; it will always be clear whether we speak about the null element or about the number zero.