let X be non empty set ; :: thesis: for S being SigmaField of X
for f being PartFunc of X,REAL
for A being Element of S st f is_measurable_on A holds
max+ f is_measurable_on A
let S be SigmaField of X; :: thesis: for f being PartFunc of X,REAL
for A being Element of S st f is_measurable_on A holds
max+ f is_measurable_on A
let f be PartFunc of X,REAL; :: thesis: for A being Element of S st f is_measurable_on A holds
max+ f is_measurable_on A
let A be Element of S; :: thesis: ( f is_measurable_on A implies max+ f is_measurable_on A )
assume f is_measurable_on A ; :: thesis: max+ f is_measurable_on A
then R_EAL f is_measurable_on A by Def6;
then max+ (R_EAL f) is_measurable_on A by MESFUNC2:25;
then R_EAL (max+ f) is_measurable_on A by Th30;
hence max+ f is_measurable_on A by Def6; :: thesis: verum