let X be non empty set ; :: thesis: for S being SigmaField of X
for f being PartFunc of X,COMPLEX
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,COMPLEX
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,COMPLEX ; :: 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 that
A1: f is_measurable_on A and
A2: f is_measurable_on B ; :: thesis: f is_measurable_on A \/ B
A3: Im f is_measurable_on B by A2, Def3;
Im f is_measurable_on A by A1, Def3;
then A4: Im f is_measurable_on A \/ B by A3, MESFUNC6:17;
A5: Re f is_measurable_on B by A2, Def3;
Re f is_measurable_on A by A1, Def3;
then Re f is_measurable_on A \/ B by A5, MESFUNC6:17;
hence f is_measurable_on A \/ B by A4, Def3; :: thesis: verum