\( \newcommand{\matr}[1] {\mathbf{#1}} \newcommand{\vertbar} {\rule[-1ex]{0.5pt}{2.5ex}} \newcommand{\horzbar} {\rule[.5ex]{2.5ex}{0.5pt}} \)
header
Show Answer
\( \newcommand{\cat}[1] {\mathrm{#1}} \newcommand{\catobj}[1] {\operatorname{Obj}(\mathrm{#1})} \newcommand{\cathom}[1] {\operatorname{Hom}_{\cat{#1}}} \)
Math and science::Analysis::Tao, measure::01. Jordan measure

Closures, interiors and Jordan measure

  1. Proof outline: see other side
  2. [Proof outline]
  3. Proof outline: see other side
  4. Proof outline: see other side

    (4), shows that Jordan outer measure (and inner measure) do not possess finite additivity for non-measurable sets. For the outer measure case, the question of what conditions might be needed to imply fintie additivity is partially answered by the Caratheodory type property.