Applying measure-theoretic results about uncountable probability spaces to discrete rational agency commits a category error between mathematical idealization and normative decision theory.
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Normative decision theory(as used in ethics and philosophy of action)
The philosophical study of how people *should* make decisions based on reason and logic, as opposed to how they actually do make them.
Uncountable probability spaces(as used in probability theory)
A mathematical setup for calculating probabilities that involves infinitely many possible outcomes so numerous they can't be listed one-by-one (like all possible real numbers between 0 and 1).