Additive Set Functions as Linear Functionals
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چکیده
We discuss the connection of additive set functions to dual function spaces by means of integrals. Isometrical isomorphisms are presented between: a) bounded contents and the dual of uniformly approximable functions, b) charges on Baire algebras and the duals of bounded, continuous functions over A-topological spaces, c) Hewitt measures on Baire σ-algebras and the duals of continuous functions over A-topological spaces. Zusammenfassung Wir behandeln die Verbindung additiver Mengenfunktionen zu dualen Funktionenräumen im Sinne des Integrals. Isometrische Isomorphismen werden vorgestellt zwischen: a) Beschränkten Inhalten und den Dualräumen gleichmäßig approximierbarer Funktionen, b) Ladungen (charges) auf Baire Algebren und den Dualräumen beschränkter, stetiger Funktionen A-topologischer Räume, c) Hewitt Maßen auf Baire σ-Algebren und den Dualräumen stetiger Funktionen Atopologischer Räume.
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