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This was proved by Kolmogorov in 1930. These papers are not to be submitted as it is. {\displaystyle {\begin{matrix}{}\\{\overline {X}}_{n}\ {\xrightarrow {P}}\ \mu \qquad {\textrm {when}}\ n\to \infty . main=0.The Definitive Checklist For Dimension The Cauchy distribution and the Pareto distribution represent two cases: the Cauchy distribution does not have