text: In the case "X" is a metric space, the Borel algebra in the first sense may be described "generatively" as follows: First define for any collection "A" of subsets of "X" (that is, for any subset of the power set P("X") of "X"), formula_1 formula_2 Then define by transfinite recursion a sequence "Gm", "m" an ordinal number, as follows: formula_3 formula_4 formula_5 Then the