Kolmogorov’s strong law of large numbers

Let X1,X2, be a sequenceMathworldPlanetmath of independentPlanetmathPlanetmath random variablesMathworldPlanetmath, with finite expectations. The strong law of large numbersMathworldPlanetmath holds if one of the following conditions is satisfied:

  1. 1.

    The random variables are identically distributed;

  2. 2.

    For each n, the variance of Xn 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