MathCS.org - Real Analysis: Example 7.3.5(c): Properties of Outer Measure

Example 7.3.5(c): Properties of Outer Measure

Outer measure is subadditive, but not additive.

Context

We need to find two disjoint sets A and B such that

m^*(A B) < m^*(A) + m^*(B)

But that is quite tricky, because most sets are measurable, and for measurable sets the above inequality turns into an equality. Unfortunately, therefore, we have to leave this statement without proof for now.

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Example 7.3.5(c): Properties of Outer Measure