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Lebesque measurable sets in R^n.

Prove that lebesque measurable sets in R^n form sigma algebra. ( Please use basic definition when you talk about the lebesgue measurable sets in R^n).

The def we have is:
(k_1)^(m)={ -1/2 + m_i =< x_i =< 1/2+ m}

m=(m_1,m_2,...,m_n)

m belongs to z^d

Now we say that A in R^n is Lebesque measurable set in R^n if

A intersection (k_1)^(m) is lebesque measurable for every m in z^d.

Solution Summary

This solution is comprised of a detailed explanation to prove that lebesque measurable sets in R^n form sigma algebra.

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