let X be non empty set ; :: thesis: for S being SigmaField of X
for f, g being PartFunc of X,REAL
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,REAL
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,REAL; :: 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 ( R_EAL f is_measurable_on A & R_EAL g is_measurable_on A ) ;
then (R_EAL f) + (R_EAL g) is_measurable_on A by MESFUNC2:7;
then R_EAL (f + g) is_measurable_on A by Th23;
hence f + g is_measurable_on A ; :: thesis: verum