let X be non empty set ; :: thesis: for S being SigmaField of X
for f being PartFunc of X,REAL
for A, B being Element of S st f is_measurable_on A & f is_measurable_on B holds
f is_measurable_on A \/ B
let S be SigmaField of X; :: thesis: for f being PartFunc of X,REAL
for A, B being Element of S st f is_measurable_on A & f is_measurable_on B holds
f is_measurable_on A \/ B
let f be PartFunc of X,REAL; :: thesis: for A, B being Element of S st f is_measurable_on A & f is_measurable_on B holds
f is_measurable_on A \/ B
let A, B be Element of S; :: thesis: ( f is_measurable_on A & f is_measurable_on B implies f is_measurable_on A \/ B )
assume ( f is_measurable_on A & f is_measurable_on B ) ; :: thesis: f is_measurable_on A \/ B
then ( R_EAL f is_measurable_on A & R_EAL f is_measurable_on B ) by Def6;
then R_EAL f is_measurable_on A \/ B by MESFUNC1:31;
hence f is_measurable_on A \/ B by Def6; :: thesis: verum