let X be non empty set ; :: thesis: for S being SigmaField of X
for f, g being PartFunc of X,COMPLEX
for A being Element of S st f is_measurable_on A & g is_measurable_on A holds
f + g is_measurable_on A
let S be SigmaField of X; :: thesis: for f, g being PartFunc of X,COMPLEX
for A being Element of S st f is_measurable_on A & g is_measurable_on A holds
f + g is_measurable_on A
let f, g be PartFunc of X,COMPLEX ; :: thesis: for A being Element of S st f is_measurable_on A & g is_measurable_on A holds
f + g is_measurable_on A
let A be Element of S; :: thesis: ( f is_measurable_on A & g is_measurable_on A implies f + g is_measurable_on A )
assume ( f is_measurable_on A & g is_measurable_on A ) ; :: thesis: f + g is_measurable_on A
then ( Re f is_measurable_on A & Im f is_measurable_on A & Re g is_measurable_on A & Im g is_measurable_on A ) by Def3;
then ( (Re f) + (Re g) is_measurable_on A & (Im f) + (Im g) is_measurable_on A ) by MESFUNC6:26;
then ( Re (f + g) is_measurable_on A & Im (f + g) is_measurable_on A ) by COM19;
hence f + g is_measurable_on A by Def3; :: thesis: verum