Independence and atoms (Q2750907)
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scientific article; zbMATH DE number 1663151
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Independence and atoms |
scientific article; zbMATH DE number 1663151 |
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Independence and atoms (English)
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21 October 2001
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independence
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atom
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purely atomic probability measure
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Borel-Cantelli lemma
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range of a probability measure
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Let \(P\) be a probability measure on a \(\sigma\)-algebra \({\mathcal A}\). The authors present an algorithm, which is hard to apply, in order to check if \({\mathcal A}\) is generated by a countable family of independent events in case \(P\) is purely atomic. They claim a consequence of this algorithm as follows: If the range \(P({\mathcal A})\) contains an interval \([0,\varepsilon]\), then \({\mathcal A}\) contains infinitely many nontrivial independent events.
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