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Outer measure, Caratheodory extension theorem

Measure \(\mu\)

Anyhow measure, nice property is liberty.
Elementary measure, nice property are monotonicyty and finite subadditivity.

Outer measure \(\mu^*\)

\(\mu^* : 2^X \rightarrow [0, +\infty]\)
\(\mu^* = inf\{ \mu_0 (\cup^\infty_{k=1} A_k): E \subset \cup^\infty_{k=1} A_j \}\)

Collection of measurable sets

Anyhow \(2^X\)
Algebra
Caratheodory