theorem Th48:
  f in x & g in x implies f a.e.= g,M & Integral(M,f) = Integral(M
  ,g) & Integral(M,abs f) = Integral(M,abs g)
proof
  assume that
A1: f in x and
A2: g in x;
A3: g in L1_Functions M by A2,Th46;
  f a.e.= g,M & f in L1_Functions M by A1,A2,Th46;
  hence thesis by A3,Th43,Th45;
end;
