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,
  c for Complex,
  E,A,B for Element of S;

theorem Th20:
  for X be non empty set, S be SigmaField of X, M be sigma_Measure
of S, f be PartFunc of X,REAL, E,A be Element of S st (ex E be Element of S st
  E = dom f & f is E-measurable) & M.A = 0 holds f|A is_integrable_on M
by Th19;
