[分析] outer measure

[pop10353 (卡卡:目)]

we have countable set outer measure zero

Q1:""Does the converse also hold?""

i.e if outer measure zero then the set is countable.

but...the outer measure empty we def zero

so we let the set be nonempty set

Q2: what the outer measure of a countable collection that each element

are countable sets? It's also zero?


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◆ From: 124.9.193.140
推 znmkhxrw    :Q1不一定 cantor set就是反例
→ znmkhxrw    :Q2的話 你的集合是"集合的集合"耶
→ pop10353    :Q2:所以不能求 集合的集合的外測度嗎？
推 znmkhxrw    :一般測度的定義是在R^n的子集
→ znmkhxrw    :所以你要定義集合的集合的外測度...自己定囉= =
→ physicist512:Q1 cantor set Q2沒有這種定義...(自己定吧@@!!)