Absolutely continuous functions on idempotent semigroups in the locally convex setting

Author:
A. Katsaras

Journal:
Trans. Amer. Math. Soc. **206** (1975), 329-337

MSC:
Primary 46E40

MathSciNet review:
0374904

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Abstract: Let be a locally convex space and let be a semigroup of semicharacters on an idempotent semigroup. It is shown that there exists an isomorphism between the space of -valued functions on and the space of all -valued finitely additive measures on a certain algebra of sets. The space of all -valued functions on which are absolutely continuous with respect to a positive definite function is identified with the space of all -valued measures which are absolutely continuous with respect to the measure corresponding to . Finally a representation is given for the operators on the set of all -valued finitely additive measures on an algebra of sets which are absolutely continuous with respect to a positive measure.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1975-0374904-2

Keywords:
Bounded variation,
absolutely continuous,
-integral,
locally convex space,
continuous seminorm,
semicharacter,
semigroup,
positive-definite,
polygonal function,
simple function,
finitely additive measure

Article copyright:
© Copyright 1975
American Mathematical Society