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

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