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What’s the big deal with Kolomgorov’s probability axioms?

https://math.stackexchange.com/questions/1431876/kolmogorovs-probability-axioms

Kolmogorov's probability axioms

Why Kolmogorov's axioms are considered such a breakthrough in probability theory? They are just 3 simple statements everyone can agree with. When creating a system of axioms like this it's necessa...

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Mehrdad Yazdani Oct 16, 2024

Relatedly: what’s a reasonable example of probability in quantum mechanics not reducible to Kolomogorov’s axioms.

https://math.stackexchange.com/questions/4489619/quantum-probability-vs-kolmogorovs-probability

Quantum probability vs. Kolmogorov's probability

It has been argued that quantum probability requires a different treatment from other random events, and a different formalization is needed than that provided by Kolmogorov's axioms. And as a phys...

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