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**Problem.**Let E be the closed unit square. Prove that every open subset of E is measurable.

I know that one way to show that a set, say A, is measurable is to show that its outer and inner measure coincide; another way is to exibit an elementary set B such that

[tex] \mu(A\Delta B)< \epsilon.[/tex]

However, I am not sure where to start. Any hints would be appreciated?