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International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 811-816
http://dx.doi.org/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 Hindawi Publishing Corporation. 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|AXandCA(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).