Abstract: More than sixty years ago these three authors proved a remarkable variant of Kolmogoroff’s law of large numbers in the iid case: a sequence of random variables $f_n$ is in $L^2$ if and only if its Cesaro averages converge “completely" to the expectation of $f_1$. We prove an extension of this result from the iid case to the case of general sequences $f_n$ in the spirit of Komlos' theorem pertaining to sequences bounded in $L^1$.
Joint with Istvan Berkes and Yannis Karatzas.