15/11/29 07:42:25.73 SasjpBzo.net
>>50-51
どうも。スレ主です。
レスありがとう！
整いました（＾＾；
ルベーグ測度、μ(S) = 0 で合意します。
さて、本題
ルベーグ測度を確認すると、定義が「・・Rn の（高々）可算個の区間からなる区間族を総称して、Rn の区間塊という。」などと、非加算には直接使えない。URLﾘﾝｸ(ja.wikipedia.org)
そこで、非加算零集合のカントール集合の扱いを参考にしようと思いつく
日wikiは、あまり詳しく書かれていないので、下記enwikiへ
URLﾘﾝｸ(en.wikipedia.org)
Cantor set
Topological and analytical properties
Although "the" Cantor set typically refers to the original, middle-thirds Cantor described above, topologists often talk about "a" Cantor set, which means any topological space that is homeomorphic (topologically equivalent) to it.
As the above summation argument shows, the Cantor set is uncountable but has Lebesgue measure 0. Since the Cantor set is the complement of a union of open sets,
it itself is a closed subset of the reals, and therefore a complete metric space. Since it is also totally bounded, the Heine?Borel theorem says that it must be compact.
For any point in the Cantor set and any arbitrarily small neighborhood of the point, there is some other number with a ternary numeral of only 0s and 2s, as well as numbers whose ternary numerals contain 1s.
Hence, every point in the Cantor set is an accumulation point (also called a cluster point or limit point) of the Cantor set, but none is an interior point.
A closed set in which every point is an accumulation point is also called a perfect set in topology, while a closed subset of the interval with no interior points is nowhere dense in the interval.
つづく