
theorem
  for X be non empty set, S be SigmaField of X, M be sigma_Measure of S,
  f be PartFunc of X,ExtREAL st (ex A be Element of S st A = dom f & f
  is A-measurable) & f is nonnegative holds 0 <= Integral(M,f)
proof
  let X be non empty set, S be SigmaField of X, M be sigma_Measure of S, f be
  PartFunc of X,ExtREAL;
  assume that
A1: ex A be Element of S st A = dom f & f is A-measurable and
A2: f is nonnegative;
  0 <= integral+(M,f) by A1,A2,Th79;
  hence thesis by A1,A2,Th88;
end;
