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
  for r be Real st 0 <= r holds (abs(f) to_power r) is
  Real-Valued-Random-Variable of Sigma
proof
  let r be Real;
  assume
A1: 0 <= r;
  abs f is nonnegative by Lm12;
  hence thesis by A1,Th23;
end;
