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Math and science::Analysis::Tao, measure::01. Jordan measure

# Closures, interiors and Jordan measure

1. Proof outline: see other side
2. [Proof outline]
3. Proof outline: see other side
4. Proof outline: see other side

(4), shows that Jordan outer measure (and inner measure) do not possess finite additivity for non-measurable sets. For the outer measure case, the question of what conditions might be needed to imply fintie additivity is partially answered by the Caratheodory type property.