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;
