Abstract

The concept of a reflexive algebra (σ-algebra) β of subsets of a set X is defined in this paper. Various characterizations are given for an algebra (σ-algebra) β to be reflexive. If V is a real vector lattice of functions on a set X which is closed for pointwise limits of functions and if β={A|A⫅X   and   CA(x)∈V} is the σ-algebra induced by V then necessary and sufficient conditions are given for β to be reflexive (where CA(x) is the indicator function).