International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 811-816
doi:10.1155/S016117128600100X
Reflexive algebras and sigma algebras
T.C. Przymusinski
and V.K. Srinivasan
Department of Mathematics, University of Texas at El Paso, El Paso 79968, Texas, USA
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).