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,ExtREAL st f is_integrable_on M & g is_integrable_on M holds
f - g is_integrable_on M
let S be SigmaField of X; :: thesis: for M being sigma_Measure of S
for f, g being PartFunc of X,ExtREAL st f is_integrable_on M & g is_integrable_on M holds
f - g is_integrable_on M
let M be sigma_Measure of S; :: thesis: for f, g being PartFunc of X,ExtREAL st f is_integrable_on M & g is_integrable_on M holds
f - g is_integrable_on M
let f, g be PartFunc of X,ExtREAL; :: thesis: ( f is_integrable_on M & g is_integrable_on M implies f - g is_integrable_on M )
assume that
A1: f is_integrable_on M and
A2: g is_integrable_on M ; :: thesis: f - g is_integrable_on M
(- jj) (#) g is_integrable_on M by A2, MESFUNC5:110;
then - g is_integrable_on M by MESFUNC2:9;
then f + (- g) is_integrable_on M by A1, MESFUNC5:108;
hence f - g is_integrable_on M by MESFUNC2:8; :: thesis: verum