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Math and science::Analysis::Tao, measure::02. Lebesgue measure

The 3 basic properties of Lebesgue outer measure 

Reminder that the Lebesgue outer measure is denoted as \( m^{*} \).

The 3 basic propositions of Lebesgue outer measure

Empty set
[...]
Monotonicity
If \( E  \subseteq F \subset \mathbb{R}^d \), then [...].
Countable subadditivity
If \( E_1, E_2, ... \subset \mathbb{R}^d \) is a countable sequence of sets, then [...]

These three ideas are very fundamental. The complex apprearance of the expressions obscures the simplicity of the ideas.