Law of Large Numbers

• If one carries out an infinite seq of independantly repeating same the same numerical mesurement and gets a sequence of measurement values $x_1,..,x_n$ where $x_i\in \mathbb{R}$, then the mean value of the inital seq upto N will almost always converge to the same number ${\mu }_N=\frac{1}{N}{\Sigma }_{i=1}^N{x}_i$ which is the EXPECTATION of X ${\mu }_N=E[X]$
• Kolmogorov axioms