I was just curious, since the B-T paradox is a measure theoretic result, if there are any consequences of this paradox in probability theory? Also, is there is a way of stating the B-T paradox in the language of probability theory?


I am ultimately interested in finding an application of the B-T paradox in physics which leads to an experimental prediction.



Applications of Banach-Tarski Paradox to Probability Theory?
I thought the whole point of having a $\sigma$-algebra for your probability space was to avoid non-measurable sets like the ones used in the proof of BT. Hence, it would seem that the BT paradox would be impossible to state in probability theory on account of the sets you need not being present in your algebra... but I might be mistaken, can someone else comment more?


