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What is the strong law of large numbers?
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A sequence of random variables $X_{1}, X_{2}, \ldots$ with finite expectations in a probability space is said to satisfiy the strong law of large numbers if
$\frac{1}{n} \sum_{k=1}^{n}\left(X_{k}-\mathrm{E}\left[X_{k}\right]\right) \stackrel{\text { a.s. }}{\longrightarrow} 0$
where a.s. stands for convergence almost surely.
When the random variables are identically distributed, with expectation $\mu$, the law becomes:
$\frac{1}{n} \sum_{k=1}^{n} X_{k} \stackrel{a . s .}{\longrightarrow} \mu$
Kolmogorov's strong law of large numbers theorems give conditions on the random variables under which the law is satisfied.
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