REPRESENTATION OF LINEAR FUNCTIONALS ON QUASI-CONTINUOUS FUNCTIONS

REPRESENTATION OF LINEAR FUNCTIONALS ON QUASI-CONTINUOUS FUNCTIONS

We prove a representation theorem for bounded linear functionals with domain the set of all real-valued, quasi-continuous functions defined on a closed interval; thus, giving a characterization of a class of bounded linear functionals.

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Veröffentlicht in:Real analysis exchange 2008-01, Vol.34 (2), p.429-444
Hauptverfasser: Vance, Joseph F, Coppin, Charles A
Format: Artikel
Sprache:eng
Schlagworte:
26A42
quasi-continuous functions
regulated functions
Stieltjes integral
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Zusammenfassung:We prove a representation theorem for bounded linear functionals with domain the set of all real-valued, quasi-continuous functions defined on a closed interval; thus, giving a characterization of a class of bounded linear functionals.
ISSN:0147-1937
1930-1219