\(
\newcommand{\cat}[1] {\mathrm{#1}}
\newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})}
\newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}}
\newcommand{\multiBetaReduction}[0] {\twoheadrightarrow_{\beta}}
\newcommand{\betaReduction}[0] {\rightarrow_{\beta}}
\newcommand{\betaEq}[0] {=_{\beta}}
\newcommand{\string}[1] {\texttt{"}\mathtt{#1}\texttt{"}}
\newcommand{\symbolq}[1] {\texttt{`}\mathtt{#1}\texttt{'}}
\newcommand{\groupMul}[1] { \cdot_{\small{#1}}}
\newcommand{\groupAdd}[1] { +_{\small{#1}}}
\newcommand{\inv}[1] {#1^{-1} }
\newcommand{\bm}[1] { \boldsymbol{#1} }
\require{physics}
\require{ams}
\require{mathtools}
\)
Math and science::Analysis::Tao, measure::02. Lebesgue measure
The 3 basic properties of Lebesgue outer measure
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.
