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
for k being positive Real st g in Lp_Functions (M,k) & g a.e.= f,M holds
g 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, g being PartFunc of X,REAL
for k being positive Real st g in Lp_Functions (M,k) & g a.e.= f,M holds
g in a.e-eq-class_Lp (f,M,k)
let M be sigma_Measure of S; :: thesis: for f, g being PartFunc of X,REAL
for k being positive Real st g in Lp_Functions (M,k) & g a.e.= f,M holds
g in a.e-eq-class_Lp (f,M,k)
let f, g be PartFunc of X,REAL; :: thesis: for k being positive Real st g in Lp_Functions (M,k) & g a.e.= f,M holds
g in a.e-eq-class_Lp (f,M,k)
let k be positive Real; :: thesis: ( g in Lp_Functions (M,k) & g a.e.= f,M implies g in a.e-eq-class_Lp (f,M,k) )
assume that
A1: g in Lp_Functions (M,k) and
A2: g a.e.= f,M ; :: thesis: g in a.e-eq-class_Lp (f,M,k)
f a.e.= g,M by A2;
hence g in a.e-eq-class_Lp (f,M,k) by A1; :: thesis: verum