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

Title	Kolmogorov’s strong law of large numbers
Canonical name	KolmogorovsStrongLawOfLargeNumbers
Date of creation	2013-03-22 13:13:12
Last modified on	2013-03-22 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