let X be non empty set ; :: thesis: for S being SigmaField of X
for M being sigma_Measure of S
for f being PartFunc of X,REAL holds f a.e.= f,M
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for f being PartFunc of X,REAL holds f a.e.= f,M
let M be sigma_Measure of S; :: thesis: for f being PartFunc of X,REAL holds f a.e.= f,M
let f be PartFunc of X,REAL; :: thesis: f a.e.= f,M
{} is Element of S by PROB_1:4;
then consider E being Element of S such that
A1: E = {} ;
A2: f | (E `) = f | (E `) ;
M . E = 0 by A1, VALUED_0:def 19;
hence f a.e.= f,M by A2; :: thesis: verum