International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 811-816
doi:10.1155/S016117128600100X
Reflexive algebras and sigma algebras
Department of Mathematics, University of Texas at El Paso, El Paso 79968, Texas, USA
Received 30 June 1985
Copyright © 1986 T. C. Przymusinski and V. K. Srinivasan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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).