Kolmogorov’s strong law of large numbers
Let ${X}_{1},{X}_{2},\mathrm{\dots}$ be a sequence^{} of independent^{} random variables^{}, with finite expectations. The strong law of large numbers^{} holds if one of the following conditions is satisfied:

1.
The random variables are identically distributed;

2.
For each $n$, the variance of ${X}_{n}$ is finite, and
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Title  Kolmogorov’s strong law of large numbers 

Canonical name  KolmogorovsStrongLawOfLargeNumbers 
Date of creation  20130322 13:13:12 
Last modified on  20130322 13:13:12 
Owner  Koro (127) 
Last modified by  Koro (127) 
Numerical id  7 
Author  Koro (127) 
Entry type  Theorem 
Classification  msc 60F15 
Synonym  Kolmogorov’s criterion 
Related topic  MartingaleProofOfKolmogorovsStrongLawForSquareIntegrableVariables 
Related topic  ProofOfKolmogorovsStrongLawForIIDRandomVariables 