theorem Th8: :: RANDOM_2:8

for Omega being non empty finite set
for f being Function of Omega,REAL
for P being Function of (bool Omega),REAL st ( for x being set st x c= Omega holds
( 0 <= P . x & P . x <= 1 ) ) & P . Omega = 1 & ( for z being finite Subset of Omega holds P . z = setopfunc (z,Omega,REAL,f,addreal) ) holds
P is Probability of Trivial-SigmaField Omega