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
for k being positive Real st f in Lp_Functions M,k holds
f in a.e-eq-class_Lp f,M,k
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for f being PartFunc of X,REAL
for k being positive Real st f in Lp_Functions M,k holds
f in a.e-eq-class_Lp f,M,k
let M be sigma_Measure of S; :: thesis: for f being PartFunc of X,REAL
for k being positive Real st f in Lp_Functions M,k holds
f in a.e-eq-class_Lp f,M,k
let f be PartFunc of X,REAL ; :: thesis: for k being positive Real st f in Lp_Functions M,k holds
f in a.e-eq-class_Lp f,M,k
let k be positive Real; :: thesis: ( f in Lp_Functions M,k implies f in a.e-eq-class_Lp f,M,k )
assume A1: f in Lp_Functions M,k ; :: thesis: f in a.e-eq-class_Lp f,M,k
f a.e.= f,M by LPSPACE1:28;
hence f in a.e-eq-class_Lp f,M,k by A1; :: thesis: verum