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On the additivity of unbounded set functions

Published online by Cambridge University Press:  17 April 2009

Brian Jefferies
Brian Jefferies
Affiliation:
School of Mathematics University of NSWP.O. Box 1 Kensington NSW 2033, Australia
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Abstract

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The set functions associated with Schrödinger's equation are known to be unbounded on the algebra of cylinder sets. However, there do exist examples of scalar valued set functions which are unbounded, yet σ-additive on the underlying algebra of sets. The purpose of this note is to show that the set functions associated with Schrödinger's equation are not σ-additive on cylinder sets. In the course of the proof, general conditions implying the non-σ-additivity of unbounded set functions are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 45 , Issue 2 , April 1992 , pp. 223 - 236
Copyright
Copyright © Australian Mathematical Society 1992

References

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