 The refinement of Bernoulli 's Golden Theorem , regarding the convergence of theoretical probability and empirical probability , was taken up by many notable later day mathematicians like De Moivre , Laplace , Poisson , Chebyshev , Markov , Borel , Cantelli , Kolmogorov and Khinchin . The complete proof of the Law of Large Numbers for the arbitrary random variables was finally provided during first half of 20th century . 
