Hi, All: I am trying to find a construction of a measurable subset that is not Borel, and ask for a ref. in this argument ( see the ***) used to show the existence of such sets: i) Every set of outer measure 0 is measurable, since: 0=m* (S)≥m*(S) , forcing equality. ii) Every subset of the Cantor set is measurable, by i), and there are 2c=22Aleph_0 such subsets. iii)*** The process of producing the Fσ , Gδ , Fσδ ,..... produces only 2Aleph_0 sets. *** iv) Since the 2 cardinalities are different, there must be a set as described in ii), i.e., a Lebesgue-measurable set that is not Borel. So, questions: 1)How do we show the process in iii) produces only c sets. 2)Anyone know of an actual construction of this set? Thanks.