Abstract:
More than seventy-five years ago, these three authors proved a remarkable variant of Kolmogorov’s Law of Large Numbers: a sequence of I.I.D. random variables $f_1, f_2, \cdots$ 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 I.I.D. case to the case of general sequences $f_1, f_2, \cdots$ in the spirit of the Komlos theorem pertaining to sequences bounded in $L^1$.
A Hereditary Hsu-Robbins-Erdös Law of Large Numbers
19.03.2025 16:45 - 19.02.2025 18:15
Organiser:
W. Schachermayer, R. Bot
Location: