:: deftheorem defines is_independent_wrt KOLMOG01:def 3 :
for Omega being non empty set
for Sigma being SigmaField of Omega
for P being Probability of Sigma
for I being set
for A being Function of I,Sigma holds
( A is_independent_wrt P iff for e being one-to-one FinSequence of I st e <> {} holds
Product ((P * A) * e) = P . (meet (rng (A * e))) );