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Real Analysis : Elementary Sets and Closure

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1) Let M be an elementary set. Prove that | closure(M)M | = 0. (closure of M can also be written as M bar, and it is the union of M and limit points of M).

2) If M and N are elementary sets then show that
| M union N | + | M intersection N| = |M| + |N|

The definition of elementary set : If M is a union of finite members of disjoint cells, then M is said to be an elementary set.

I believe it is related to lebesgue measure topics, but not so sure.

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Solution Summary

Elementary Sets and Closure are investigated. The solution is detailed and well presented.

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