ON MARCINKIEWICZ-ZYGMUND LAWS OF LARGE NUMBERS IN
BANACH SPACES AND RELATED RATES OF CONVERGENCE
Abstract: The paper studies asymptotic almost sure and tail behavior of sums
for independent, centered random vectors
taking values in Banach space . The obtained results are in the spirit of
Mazurkiewicz-Zygmund, Hsu-Robbins-Erdös-Spitzer, and Brunk theorems for real
random variables and show the essential role played by the geometry of in the
infinite-dimensional case.
2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -