Question

F inverse of measurable set is measurable implies function is measurable proof

Answer 1

. I just saw that the statement "The inverse image of a measurable set under a measurable function is measurable" is false with counter-example the function on Cantor set but I know the definition of f measurable is:

Let f:(X,OX)→(Y,OY) with OX σ-algebra of X and OY σ-algebra of Y. f said (OX−OY)-measurable function if for all B∈OY f−1(B)∈OX.

But, What is the difference with "The inverse image of a measurable set under a measurable function is measurable? "