strong law of large numbers

A sequence of random variablesMathworldPlanetmath X1,X2, with finite expectations in a probability spaceMathworldPlanetmath is said to satisfiy the strong law of large numbersMathworldPlanetmath if


where a.s. stands for convergence almost surely.

When the random variables are identically distributed, with expectation μ, the law becomes:


Kolmogorov’s strong law of large numbers theorems give conditions on the random variables under which the law is satisfied.

Title strong law of large numbers
Canonical name StrongLawOfLargeNumbers
Date of creation 2013-03-22 13:13:10
Last modified on 2013-03-22 13:13:10
Owner Koro (127)
Last modified by Koro (127)
Numerical id 11
Author Koro (127)
Entry type Definition
Classification msc 60F15
Related topic MartingaleProofOfKolmogorovsStrongLawForSquareIntegrableVariables