
theorem Th43:
  for X be non empty set, S be SigmaField of X, M be sigma_Measure
  of S, A be Element of S, f,g being PartFunc of X,ExtREAL st A c= dom f & f
  is A-measurable & g is A-measurable & f is without-infty & g is
  without-infty holds max+(f+g) + max-f is A-measurable
proof
  let X be non empty set, S be SigmaField of X, M be sigma_Measure of S, A be
  Element of S, f,g be PartFunc of X,ExtREAL;
  assume that
A1: A c= dom f and
A2: f is A-measurable and
A3: g is A-measurable and
A4: f is without-infty and
A5: g is without-infty;
  f+g is A-measurable by A2,A3,A4,A5,Th31;
  then
A6: max+(f+g) is A-measurable by MESFUNC2:25;
A7: max-f is nonnegative by Lm1;
A8: max+(f+g) is nonnegative by Lm1;
  max-f is A-measurable by A1,A2,MESFUNC2:26;
  hence thesis by A6,A8,A7,Th31;
end;
