
theorem
  for k1,k2 being Real holds ].k1,k2.] is Event of Borel_Sets
  proof
    let k1,k2 be Real;
A1: [.k1,k2.] is Element of Borel_Sets by FINANCE1:8;
A2: {k1} is Event of Borel_Sets by Th1;
    reconsider k1,k2 as ExtReal;
    per cases;
    suppose B1: k1<=k2;
      [.k1,k2.] \ {k1} is Element of Borel_Sets by A1,A2,PROB_1:24;
      hence thesis by B1,XXREAL_1:134;
    end;
    suppose k1>k2; then
      ].k1,k2.]={} by XXREAL_1:26;
      hence thesis by PROB_1:4;
    end;
  end;
