Reflexive algebras and sigma algebras
Teodor C. Przymusiński, V.K. Srinivasan · International Journal of Mathematics and Mathematical Sciences · 1986
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).