
theorem
  for a be Real holds {a} is thin of B-Meas
proof
    let a be Real;
    set A = [.a,a.];
    reconsider E = {a} as Subset of REAL;
A1: A in Family_of_Intervals by MEASUR10:def 1;
A2: Family_of_Intervals c= Field_generated_by Family_of_Intervals
      by SRINGS_3:21;
A3: Field_generated_by Family_of_Intervals c= Borel_Sets
      by PROB_1:def 9,MEASUR10:6;
A4: E c= A by XXREAL_1:17;
    reconsider a1 = a as R_eal by XXREAL_0:def 1;
    B-Meas.A = diameter A by Th72 .= a1 - a1 by MEASURE5:6
     .= a - a by Lm9 .= 0;
    hence {a} is thin of B-Meas by A3,A2,A1,A4,MEASURE3:def 2;
end;
