Measure and integration: The basic extension and representation theorems in terms of new inner and outer envelopes |
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Authors: | Heinz König |
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Institution: | Universität des Saarlandes, Fakultät für Mathematik und Informatik, D-66041 Saarbrücken, Germany |
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Abstract: | The work of the author in measure and integration is based on new inner and outer envelope formations, which replace the traditional Carathéodory outer measure and certain simple suprema and infima. The new formations lead to essential improvements in both the extent and the adequacy of the basic results. However, they did not find an entrance into the recent textbook literature. The present paper seeks to demonstrate their power with the examples of the basic inner and outer extension and representation theorems for set functions and functionals. |
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Keywords: | Inner and outer premeasures Inner and outer envelopes of set functions and functionals Inner and outer extension and representation theorems Choquet integral Carathé odory class |
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