2
$\begingroup$

Is there a version of the 0-1-law that applies as well to non-measurable sets? (I.e., a proof that doesn't presume the set under consideration to be measurable.)

  • 1
    what is then the probability measure of the non-measurable set? If it is a null-set (i.e. the subset of the set of measure zero) then this law will work if you complete the measure: http://en.wikipedia.org/wiki/Complete_measure2011-10-10
  • 0
    It could be that the complement of the set is the null-set, or that we don't know which of the two is a null-set. Perhaps a hlpful reformulation: does there exist a non-measurable subset S \subset of [0,1] such that for every natural k: if |x - y| = 1/2^k, then x \in S iff y \in S ?2011-10-10

2 Answers 2