
theorem Th15:
for X be non empty set, S be SigmaField of X,
 A,B,C be Element of S, er be ExtReal st C c= B holds
   chi(er,A,X)|B is C-measurable
proof
   let X be non empty set, S be SigmaField of X,
   A,B,C be Element of S, er be ExtReal;
   assume a1: C c= B;
   dom chi(er,A,X) = X by FUNCT_2:def 1; then
B: B = dom chi(er,A,X) /\ B by XBOOLE_1:28;
   chi(er,A,X) is B-measurable by Th13; then
   chi(er,A,X)|B is B-measurable by MESFUNC5:42,B;
   hence thesis by a1,MESFUNC1:30;
end;
