reserve X for set,
  F for Field_Subset of X,
  M for Measure of F,
  A,B for Subset of X,
  Sets for SetSequence of X,
  seq,seq1,seq2 for ExtREAL_sequence,
  n,k for Nat;
reserve FSets for Set_Sequence of F,
  CA for Covering of A,F;
reserve Cvr for Covering of Sets,F;

theorem Th11:
  (C_Meas M).{} = 0
proof
  (C_Meas M).{} <= M.{} by Th9,PROB_1:4;
  then
A1: (C_Meas M).{} <= 0 by VALUED_0:def 19;
  {}X in bool X;
  then {} in dom(C_Meas M) by FUNCT_2:def 1;
  then
A2: (C_Meas M).{} in rng C_Meas M by FUNCT_1:3;
  C_Meas M is nonnegative by Th10;
  then rng C_Meas M is nonnegative;
  hence (C_Meas M).{} = 0. by A1,A2;
end;
