15/11/28 23:37:17.69 novsUjda.net
>>48
どうも。スレ主です。
ご指摘の通りです。そう考えてます
でも、、「超越基底Sが、可測集合か？」ってところが問題なのか
零集合は、必ずしもルベーグ可測には限らないようだが、ルベーグ可測と密接に関係している・・（下記）
いやー、むずいねー（＾＾；
「超越基底Sが、可測集合」が言えれば、”Given any positive number ε, there is a sequence {In} of intervals in R such that N is contained in the union of the {In} and the total length of the union is less than ε. ”みたいな論法が使えるかも（＾＾；
どうなんだろ
URLﾘﾝｸ(en.wikipedia.org)
In set theory, a null set N ⊂ R is a set that can be covered by an countable union of intervals of arbitrarily small total length. The notion of null set in set theory anticipates the development of Lebesgue measure since a null set necessarily has measure zero.
Lebesgue measure
The Lebesgue measure is the standard way of assigning a length, area or volume to subsets of Euclidean space.
A subset N of R has null Lebesgue measure and is considered to be a null set in R if and only if:
Given any positive number ε, there is a sequence {In} of intervals in R such that N is contained in the union of the {In} and the total length of the union is less than ε.
For instance:
With respect to Rn, all 1-point sets are null, and therefore all countable sets are null. In particular, the set Q of rational numbers is a null set, despite being dense in R.
The standard construction of the Cantor set is an example of a null uncountable set in R; however other constructions are possible which assign the Cantor set any measure whatsoever.