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MrMind comments on Open Thread, Jul. 27 - Aug 02, 2015 - Less Wrong
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This is an old problem in probability theory, and there are different solutions.
PT is developed first in finite model, so it's natural that its extension to infinite models can be done in a few different ways.
Could you point me to some solutions?
They have already been pointed to you: either extend PT to use some kind of measure (Jaynes' solution), ore use only distributions that have a definite limit when extended to the infinite, or use infinitely small quantities.