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Proceedings of the American Mathematical Society

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

 
 

 

Signed quasi-measures and dimension theory


Author: D. J. Grubb
Journal: Proc. Amer. Math. Soc. 128 (2000), 1105-1108
MSC (1991): Primary 28C15
DOI: https://doi.org/10.1090/S0002-9939-99-05093-5
Published electronically: August 5, 1999
MathSciNet review: 1636950
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Abstract: A quasi-linear functional on $C(X)$ is a real-valued function that is linear on each closed, singly generated subalgebra and is norm bounded. We show that if the covering dimension $\dim X\leq 1$, then every quasi-linear functional on $C(X)$ is, in fact, linear. We do this by considering an associated set function, called a quasi-measure, and ask when such a set function can be extended to be a measure.


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Additional Information

D. J. Grubb
Affiliation: Department of Mathematical Sciences, Northern Illinois University, De Kalb, Illinois 60115
Email: grubb@math.niu.edu

DOI: https://doi.org/10.1090/S0002-9939-99-05093-5
Received by editor(s): February 10, 1998
Received by editor(s) in revised form: June 1, 1998
Published electronically: August 5, 1999
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society