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Probability and statistics in Italy during the First World War I: Cantelli and the laws of large numbers

Some of the most important Italian contributions to probability and statistics came to light in the WW1 years 1915-1918: the Cantelli’s theory of stochastic convergence together with the first correct and (rather) general version of the strong law of large numbers, and the Gini theory of statistical association. These studies were influential in determining the characteristics of the subsequent developments of the statistical and probabilistic research in Italy. The present paper is the first part of an article that aims at describing the spirit of these studies, and helping readers understand their connections both with pre-existent and contemporary literature. It is devoted to the contributions of Cantelli. The (future) second part will deal with statistics and, in particular, with Gini’s works on statistical association.