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 st f in L1_Functions M holds
f in a.e-eq-class (f,M)
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for f being PartFunc of X,REAL st f in L1_Functions M holds
f in a.e-eq-class (f,M)
let M be sigma_Measure of S; :: thesis: for f being PartFunc of X,REAL st f in L1_Functions M holds
f in a.e-eq-class (f,M)
let f be PartFunc of X,REAL; :: thesis: ( f in L1_Functions M implies f in a.e-eq-class (f,M) )

hereby :: thesis: verum

assume A1: f in L1_Functions M ; :: thesis: f in a.e-eq-class (f,M)
f a.e.= f,M by Th28;
hence f in a.e-eq-class (f,M) by A1; :: thesis: verum

end;