let X be non empty set ; :: thesis: for S being SigmaField of X
for f being PartFunc of X,COMPLEX
for A being Element of S st f is_simple_func_in S holds
f is_measurable_on A
let S be SigmaField of X; :: thesis: for f being PartFunc of X,COMPLEX
for A being Element of S st f is_simple_func_in S holds
f is_measurable_on A
let f be PartFunc of X,COMPLEX ; :: thesis: for A being Element of S st f is_simple_func_in S holds
f is_measurable_on A
let A be Element of S; :: thesis: ( f is_simple_func_in S implies f is_measurable_on A )
assume f is_simple_func_in S ; :: thesis: f is_measurable_on A
then ( Re f is_simple_func_in S & Im f is_simple_func_in S ) by MESFUN7C:43;
then ( Re f is_measurable_on A & Im f is_measurable_on A ) by MESFUNC6:50;
hence f is_measurable_on A by MESFUN6C:def 3; :: thesis: verum