Abstract: Let be an exchangeable sequence of
r.v.’s defined on a probability space We assume that and prove a Kolmogorov’s type
inequality for this sequence. Using the inequality we give an alternative proof
of the Strong Law of Large Numbers for sucha
sequence. An immediate consequence is the well-known Strong Lawof Large Numbers for a sequence of independent and identically
distributed r.v.’s, such that In the process of proving theabove results, we also prove (basic) properties of exchangeable r.v.’s.
All these results are proved in a unified martingale approach.
Keywords and phrases: exchangeable sequences, symmetric measures, Kolmogorov’s inequality, martingales, strong law of large numbers.
