Question

Show that the collection of all measurable sets contains the collection of all borel sets

Answer 1

χA: characteristic function of A.

χA(x)=1 if x∈A , χA(x)=0 if x∉A,

I need to find or prove the existence of a sequence of positive continuous functions, increasing to converge to χA, then I could use the basic theorem of measure theory to put all the functions borel measurable in the set. Any help is appreciated, I try with step functions but dont result.