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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Extremal and monogenic additive set functions


Author: Detlef Plachky
Journal: Proc. Amer. Math. Soc. 54 (1976), 193-196
MSC: Primary 28A10
DOI: https://doi.org/10.1090/S0002-9939-1976-0419711-3
MathSciNet review: 0419711
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Abstract: The extreme points of the convex set of all additive set functions on a field, which coincide on a subfield are characterized by a simple approximation property. It is proved that a stronger approximation property is characteristic for a so-called monogenic additive set function on a field, which can be generated uniquely by an additive set function on a subfield. Finally it is shown that a simple decomposition property must hold if the convex set above has a finite number of extreme points.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1976-0419711-3
Keywords: Extreme points, finitely additive set functions, $ \{ 0,1\} $-valued set functions, Baire resp. Borel measures
Article copyright: © Copyright 1976 American Mathematical Society