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 f in Lp_Functions M,k & g in Lp_Functions M,k holds
f - g in Lp_Functions 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 f in Lp_Functions M,k & g in Lp_Functions M,k holds
f - g in Lp_Functions M,k
let M be sigma_Measure of S; :: thesis: for f, g being PartFunc of X,REAL
for k being positive Real st f in Lp_Functions M,k & g in Lp_Functions M,k holds
f - g in Lp_Functions M,k
let f, g be PartFunc of X,REAL ; :: thesis: for k being positive Real st f in Lp_Functions M,k & g in Lp_Functions M,k holds
f - g in Lp_Functions M,k
let k be positive Real; :: thesis: ( f in Lp_Functions M,k & g in Lp_Functions M,k implies f - g in Lp_Functions M,k )
assume A1: ( f in Lp_Functions M,k & g in Lp_Functions M,k ) ; :: thesis: f - g in Lp_Functions M,k
then (- 1) (#) g in Lp_Functions M,k by Th01bLp;
hence f - g in Lp_Functions M,k by Th01aLp, A1; :: thesis: verum