Q:

Prove that if and for each , then is lebesgue measurable. ( is the -algebra of Lebesgue measurable sets)

Attempt:

I need to show that for any set , (is this correct?). So I take a set . By definition of , is an open interval (is this correct?). Now, i want to write as a union of sets of the form for each but im sturggling to do this! Is this the right method? Can you help me? Thank you