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strong law of large numbers
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(Definition)
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"strong law of large numbers" is owned by Koro.
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(view preamble)
Cross-references: Kolmogorov's strong law of large numbers, identically distributed, almost surely, numbers, probability space, expectations, finite, random variables, sequence
There are 2 references to this entry.
This is version 8 of strong law of large numbers, born on 2002-12-08, modified 2006-09-28.
Object id is 3685, canonical name is StrongLawOfLargeNumbers.
Accessed 6848 times total.
Classification:
| AMS MSC: | 60F15 (Probability theory and stochastic processes :: Limit theorems :: Strong theorems) |
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Pending Errata and Addenda
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![$\displaystyle \frac{1}{n}\sum_{k=1}^n (X_k -\operatorname{E}[X_k]) \xrightarrow[]{a.s.} 0, $](http://images.planetmath.org:8080/cache/objects/3685/l2h/img2.png "$\displaystyle \frac{1}{n}\sum_{k=1}^n (X_k -\operatorname{E}[X_k]) \xrightarrow[]{a.s.} 0, $")
![$\displaystyle \frac{1}{n}\sum_{k=1}^n X_k\xrightarrow[]{a.s.} \mu.$](http://images.planetmath.org:8080/cache/objects/3685/l2h/img5.png "$\displaystyle \frac{1}{n}\sum_{k=1}^n X_k\xrightarrow[]{a.s.} \mu.$")