let Omega be non empty set ; :: thesis: for Sigma being SigmaField of Omega
for ASeq being SetSequence of Sigma
for P being Probability of Sigma st ASeq is disjoint_valued holds
P . (Union ASeq) = Sum (P * ASeq)
let Sigma be SigmaField of Omega; :: thesis: for ASeq being SetSequence of Sigma
for P being Probability of Sigma st ASeq is disjoint_valued holds
P . (Union ASeq) = Sum (P * ASeq)
let ASeq be SetSequence of Sigma; :: thesis: for P being Probability of Sigma st ASeq is disjoint_valued holds
P . (Union ASeq) = Sum (P * ASeq)
let P be Probability of Sigma; :: thesis: ( ASeq is disjoint_valued implies P . (Union ASeq) = Sum (P * ASeq) )
assume ASeq is disjoint_valued ; :: thesis: P . (Union ASeq) = Sum (P * ASeq)
then lim (Partial_Sums (P * ASeq)) = P . (Union ASeq) by Th45;
hence P . (Union ASeq) = Sum (P * ASeq) by SERIES_1:def 3; :: thesis: verum