Limitations on the extendibility of the Radon-Nikodym Theorem

Author:
Gerd Zeibig

Journal:
Proc. Amer. Math. Soc. **131** (2003), 2491-2500

MSC (2000):
Primary 46B22; Secondary 46J10, 46E30

DOI:
https://doi.org/10.1090/S0002-9939-03-07046-1

Published electronically:
March 11, 2003

MathSciNet review:
1974647

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Abstract | References | Similar Articles | Additional Information

Abstract: Given two locally compact spaces and a continuous map the Banach lattice is naturally a -module. Following the Bourbaki approach to integration we define generalized measures as -linear functionals . The construction of an -space and the concepts of absolute continuity and density still make sense. However we exhibit a counter-example to the natural generalization of the Radon-Nikodym Theorem in this context.

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Additional Information

**Gerd Zeibig**

Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, Ohio 44240

Email:
gzeibig@math.kent.edu

DOI:
https://doi.org/10.1090/S0002-9939-03-07046-1

Keywords:
Banach module,
Radon-Nikodym Theorem,
Riesz Theorem

Received by editor(s):
March 20, 2002

Published electronically:
March 11, 2003

Communicated by:
N. Tomczak-Jaegermann

Article copyright:
© Copyright 2003
American Mathematical Society