let X be non empty set ; :: thesis: for S being SigmaField of X
for M being sigma_Measure of S
for f, g being PartFunc of X,REAL st f a.e.= g,M holds
g a.e.= f,M
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for f, g being PartFunc of X,REAL st f a.e.= g,M holds
g a.e.= f,M
let M be sigma_Measure of S; :: thesis: for f, g being PartFunc of X,REAL st f a.e.= g,M holds
g a.e.= f,M
let f, g be PartFunc of X,REAL ; :: thesis: ( f a.e.= g,M implies g a.e.= f,M )
assume f a.e.= g,M ; :: thesis: g a.e.= f,M
then ex E being Element of S st
( M . E = 0 & f | (E ` ) = g | (E ` ) ) by Def2;
hence g a.e.= f,M by Def2; :: thesis: verum