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

[1] https://omnicognate.wordpress.com/2013/11/04/sigma-algebras-...