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Proceedings of the American Mathematical Society

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

 

 

Representation of linear functionals on quasi-continuous functions


Author: James D. Baker
Journal: Proc. Amer. Math. Soc. 48 (1975), 120-124
MSC: Primary 46E15
DOI: https://doi.org/10.1090/S0002-9939-1975-0374884-5
MathSciNet review: 0374884
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Abstract: The question of representing the continuous linear functionals on the complex quasi-continuous functions in terms of a single integral of Stieltjes type is considered. An integral on three functions is defined, is shown to provide a unique representation of the functionals, and in special cases, is shown to reduce to standard Stieltjes integrals involving two functions.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0374884-5
Keywords: Stieltjes integrals, quasi-continuous functions, linear functionals
Article copyright: © Copyright 1975 American Mathematical Society