reserve X for non empty set,
  Y for set,
  S for SigmaField of X,
  M for sigma_Measure of S,
  f,g for PartFunc of X,COMPLEX,
  r for Real,
  k for Real,
  n for Nat,
  E for Element of S;

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;
