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Artusartos

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## Homework Statement

Let E have finite outer measure. Show that if E is not measurable, then there is an open set O containing E that has finite measure and for which

m*(O~E) > m*(O) - m*(E)

## Homework Equations

## The Attempt at a Solution

This is what I did...

[itex]m^*(O) = m^*((O \cap E^c) \cup m^*((O \cap E)) \leq m^*(O \cap E^c) + m^*(E)[/itex]

So...

[itex]m^*(O) - m^*(E) \leq m^*(O \cap E^c)[/itex]

But I'm confused about the equality, because the one in the question is a strict inequality

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