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john33

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    Help with some Lebesgue measure problems

    john33 posted a topic in Analysis and Calculus
    Hi everyone, I'm trying to solve some Lebesgue problems from my exercise book and I got stuck in some of them: Prove that if a set A has zero measure, then its interior is empty. I've thinking on suppose the contrary and find an open subset of A with positive measure, but I'm not really sure if it's the right way. True or false: f is integrable if and only if |f| is integrable over Rn. I know that if f is measurable, then it's correct, but here there is no previous condition so I don't know if the statement is true or false. Could you give me some tips to solve it? Thanks in advance.

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