reserve X for set;
reserve X,X1,X2 for non empty set;
reserve S for SigmaField of X;
reserve S1 for SigmaField of X1;
reserve S2 for SigmaField of X2;
reserve M for sigma_Measure of S;
reserve M1 for sigma_Measure of S1;
reserve M2 for sigma_Measure of S2;

theorem Th9:
for E being Element of S, f be E-measurable PartFunc of X,ExtREAL
 st dom f = E holds eq_dom(f,+infty) in S & eq_dom(f,-infty) in S
proof
   let E be Element of S, f be E-measurable PartFunc of X,ExtREAL;
   assume A1: dom f = E; then
A2:eq_dom(f,+infty) c= E & eq_dom(f,-infty) c= E by MESFUNC1:def 15;
   E /\ eq_dom(f,+infty) in S & E /\ eq_dom(f,-infty) in S
     by A1,MESFUNC1:33,34;
   hence thesis by A2,XBOOLE_1:28;
end;
