let X be non empty set ; :: thesis: for S being SigmaField of X
for f being PartFunc of X,REAL
for B, A being Element of S st B c= A & f is_measurable_on A holds
f is_measurable_on B
let S be SigmaField of X; :: thesis: for f being PartFunc of X,REAL
for B, A being Element of S st B c= A & f is_measurable_on A holds
f is_measurable_on B
let f be PartFunc of X,REAL; :: thesis: for B, A being Element of S st B c= A & f is_measurable_on A holds
f is_measurable_on B
let B, A be Element of S; :: thesis: ( B c= A & f is_measurable_on A implies f is_measurable_on B )
assume that
A1: B c= A and
A2: f is_measurable_on A ; :: thesis: f is_measurable_on B
R_EAL f is_measurable_on A by A2, Def6;
then R_EAL f is_measurable_on B by A1, MESFUNC1:30;
hence f is_measurable_on B by Def6; :: thesis: verum