reserve Omega for non empty set;
reserve r for Real;
reserve Sigma for SigmaField of Omega;
reserve P for Probability of Sigma;
reserve E for finite non empty set;
reserve f,g for Real-Valued-Random-Variable of Sigma;

theorem Th24:
  abs f is Real-Valued-Random-Variable of Sigma
proof
A2: f is ([#]Sigma)-measurable;
  dom f = [#]Sigma & R_EAL f is ([#]Sigma)-measurable by A2,FUNCT_2:def 1;
  then |.R_EAL f.| is ([#]Sigma)-measurable by MESFUNC2:27;
  then R_EAL abs(f) is ([#]Sigma)-measurable by MESFUNC6:1;
  then abs(f) is ([#]Sigma)-measurable;
  hence thesis;
end;
