Aspects on the law of large numbers
Allan Gut, Uppsala University,
Uppsala, Sweden

This year, the year of statistics, we celebrate the 300 year anniversary of the appearance of Ars conjectandi, where we nd the rst proof of the weak law of large numbers, although only for coin-tossing variables. We also celebrate the equally old St. Petersburg paradox, which nowadays, after Feller's solution in 1945, has turned into the St. Petersburg game.

Last but not least, this year marks 80 years since the appearance of Kolmogorov's famous Grundbegri e der Wahrscheinlichkeitsrechnung, where the foundation and axio- matization of the theory of probability was laid. A short discussion on the strong law of large numbers concludes the treatise.

In this talk I will present a survey of the St. Petersburg game, on various aspects of the law of large numbers, and provide an outlook on some extensions and generalizations.

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