Decomposition and Extension of Abstract Measures in Riesz Spaces
Decomposition and Extension of Abstract Measures in Riesz Spaces
This paper is based on some lectures given during the Workshop of Measure Theory and Real Analysis held at Grado in September 1995. The main aim of the paper is to present a common approach to vector measures and linear operators. For that, the author first studies ``minimal clans'', a common abstraction of Boolean rings and \(\ell\)-groups, and then decomposition theorems for additive functions on minimal clans. As special cases, the author obtains decomposition theorems for vector measures and for linear operators. Moreover, the paper deals with common extension of linear operators and common extension of vector measures.
- University of Mannheim Germany
- University of Trieste Italy
linear operators, decomposition theorems, minimal clans, vector measures, Vector-valued set functions, measures and integrals, Vector-valued measures and integration, common extensions, 510
linear operators, decomposition theorems, minimal clans, vector measures, Vector-valued set functions, measures and integrals, Vector-valued measures and integration, common extensions, 510
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