theorem Th7:
  for X be non empty set, f be with_the_same_dom
    Functional_Sequence of X,REAL
  for S be SigmaField of X, E be Element of S, n be Nat st
    f.n is E-measurable holds (R_EAL f).n is E-measurable
proof
  let X be non empty set, f be with_the_same_dom Functional_Sequence of X,REAL;
  let S be SigmaField of X, E be Element of S, n be Nat;
  assume f.n is E-measurable;
  then R_EAL(f.n) is E-measurable by MESFUNC6:def 1;
  hence thesis;
end;
