E is measurable then it's complement is also measurable

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first we need a definition of measurable set and one important theorem E is measurable iff this inequality hold

E is measurable iff inequality holds

Measurable set

Outer measure is countably subaddtive

Outer measure

Example of Outermeasure

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complement of measurable set is measurable

ii) The complement of any measurable set is measurable. iii) The union of a countable collection of measurable sets is measurable. ... Definition: The collection M of Lebesgue measurable subsets of R is the smallest σ-algebra that contains all open intervals (a, b) ⊂ R.
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