Kolmogorov's inequality

The Kolmogorov 's inequality is a so-called maximal inequality from the stochastics. It was demonstrated in the late 1920s by the Russian mathematician Andrei Nikolaevich Kolmogorov and serves to prove a strong law of large numbers for random variables, which must be distributed not necessarily identical, but follow the kolmogorowschen criterion.

Your statement

The Kolmogorov 's inequality says that applies to a sequence of independent random variables with the following for each Maximalungleichung:

Denotes the - th partial sum.