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The concept of probability is based on the concept of measure in math => limitation in its description of things, e.g., the probability for a real number in [0,
by quantum_state 3y ago
The concept of probability is based on the concept of measure in math => limitation in its description of things, e.g., the probability for a real number in [0, 1) being an irrational number is 1.
- eli_gottlieb 3y agoHold 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 even form a proper measurable set?
- omnicognate 3y agoLebesgue 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 agoThe irrationals are measurable for any measure that can measure points, which is most of them.
- hgsgm 3y agoOf course. [0,1] has measure 1. Rationals have measure 0. Irrationals have measure 1-0=1 This question is why measure theory exists.