Measure 성질 type 분류

1. Set operation
(1)closed under complement
(2)closed under ctb union(fnt union보다 강력)
(3)closed under ctb intersection(fnt intersection보다 강력)

(4)closed under difference

2. monotone

(1) subset이 measure 작아야, 항상 필요, 그래야 직관적임에 부합되지

(2) continuity for ascending, or descending measurable sets

(closed under union or closed under intersection일 때 논의가능)

3. additivity

(1)ctb add(fnt add보다 강력)

(2)ctb subadd(fnt subadd보다 강력)

(monotone이 보장되면 ctb add->ctb subadd)

4. Approximation by simpler

(1) Jordan<-Elementary sets

(2) L-measurable<-by open sets or closed sets or compact set

5. 기타

(1) Translation invariance, Closure invariance, Interior Invariance, Linear Transformation Invariance

(2) Related to Integrability of characteristic function(Jordan<->Riemann, Lebesgue measurable set<->Lebesgue Integration)

(3) any subset of measurable set, 의 outer measure, inner measure

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