4 ms·

Hold on, what measure over the unit interval assigns probability 1 to the set of irrational numbers in the unit interval? Do irrational numbers on their own ev

• omnicognate 3y ago
  Lebesgue measure [0]. I never did write part 2 and many years have gone by with that blog languishing unmaintained on free wordpress but I wrote a thing that goes through the issues around this [1]. [0] https://en.m.wikipedia.org/wiki/Lebesgue_measure https://en.m.wikipedia.org/wiki/Lebesgue_measure [1] https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-and-filtrations-in-probability-theory-part-1 https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-...
• contravariant 3y ago
  The irrationals are measurable for any measure that can measure points, which is most of them.
• hgsgm 3y ago
  Of course. [0,1] has measure 1. Rationals have measure 0. Irrationals have measure 1-0=1 This question is why measure theory exists.