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       C A ( x ) ∈ V } is the σ -algebra induced by V then necessary and sufficient conditions are given for β to be reflexive (where C A ( x ) is the indicator function).