## 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