Abstract
Measurable sets are defined as those locally approximable, in a certain sense, by sets in the given algebra (or ring). A corresponding measure extension theorem is proved. It is also shown that a set is locally approximable in the mentioned sense if and only if it is Carathéodory-measurable.
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References
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Pinelis, I. Measure extension by local approximation. Positivity 22, 199–208 (2018). https://doi.org/10.1007/s11117-017-0507-8
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DOI: https://doi.org/10.1007/s11117-017-0507-8
Keywords
- Measures
- Measure extension
- Rings of sets
- Algebras of sets
- Sigma-algebras of sets
Mathematics Subject Classification
- 28A12
- 60A10