Measure and integration Measures Concept
Countable additivity
Summary
A set function is countably additive, or σ-additive, if its value on a countable disjoint union is the sum of its values on the pieces. Countable additivity is the defining property of measures. It is stronger than finite additivity, and it is what makes limit theorems such as monotone convergence work.
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About this page
| Tag | D7KB9HFCGZ |
|---|---|
| URI | m2://D7KB9HFCGZ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 28A10 |
| Same as | |
| Changed | 2 November 2026 |
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Used by
- Finitely additive measure
- Measure
- Signed measure
- Nikodym convergence theorem
- Continuity of measure from below and above
- Measure problem of Lebesgue
- Complex measure