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I have two problems that I would like some help with.

  1. Show that every countable subset of $\mathbb{R}$ has Lebesgue measure zero.

  2. For two arbitrary sets $A$ and $B$ show that $$\lvert m^*(A)-m^*(B)\rvert \leq m^*(A \triangle B)$$ where $\triangle$ is the symmetric difference operator.

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    You should post your two problems as two separate questions.2012-10-18

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