Let X=[0,1] , A= . (B is the Borel- algebra), the lebesgue measure. In explain why these statements are true or false:

1) if with and then

2) if and then

Well I honestly do not have much ideas how to solve this. It's clear 1) isn't true because 2) wouldn't make sense if 1) was true. But a formal explanation? A prove? I don't know.

All I tried was finding functions that are for example in L_1 but not in L_2 . But I couldn't find a contradiction. Also there exist Lebesgue-integrable functions that are not bounded...??

Could please someone give me a hint?