Graeme Keith
Mar 25, 2021

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That's a really interesting point. I guess you're right in the sense that the elements are measurable in the mathematical sense, sure. But its not clear that you can actually measure in the practical sense everything in the sigma field, even if you wanted to (and in principle could) and also you can easily construct sigma algebras that have far fewer elements than everything that is, in principle, measurable. The odd / even outcomes on the die being a case in point (empty, odd, even, full) is a sigma algebra, but there are many more measurable outcomes. It was in this latter sense that I went with what you want to know, but I definitely see your point. Most Borel algebra have far more structure than anything I'd realistically ever want to know!

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Graeme Keith
Graeme Keith

Written by Graeme Keith

Mathematical modelling for business and the business of mathematical modelling. See stochastic.dk/articles for a categorized list of all my articles on medium.

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