reserve Omega for non empty set;
reserve Sigma for SigmaField of Omega;
reserve S for non empty Subset of REAL;
reserve r for Real;
reserve T for Nat;
reserve I for TheEvent of r;

theorem Th3:
  for k being Real holds
  ].k,+infty.] is Element of Ext_Borel_Sets &
  [.-infty,k.] is Element of Ext_Borel_Sets
proof
 let k be Real;
A3: [.-infty,k.] in Ext_Family_of_halflines;
a2: Ext_Family_of_halflines c= sigma(Ext_Family_of_halflines) by PROB_1:def 9;
 ExtREAL in Ext_Borel_Sets by PROB_1:5;
 then ExtREAL\[.-infty,k.] in Ext_Borel_Sets by a2,PROB_1:6,A3;
 hence thesis by Th2,a2,A3;
end;
