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    Restricting to countable additivity is itself a conventio... — Carmelics
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    Challenges→Continuous probability distributions require a restriction to countable additivity rather than full additivity

    Restricting to countable additivity is itself a conventional stipulation, not a mathematical necessity, as Dubins and Savage showed in 'How to Gamble If You Must' (1965).

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    Reasons For

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    Reason for
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    • 1.Finitely additive measures on infinite spaces are mathematically consistent and avoid Kolmogorov's countable additivity requirement.
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    • 2.Dubins-Savage theory demonstrates gambling strategies viable under finitely additive probability without contradicting rational decision theory.
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    • 3.Scientific practice often succeeds with non-countably-additive models, suggesting countability isn't empirically necessary for applications.
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    Reasons Against

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    Reason against
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    • 1.Countable additivity is forced by topology and measure-theoretic limits, not mere convention; it's foundational to modern analysis itself.
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    • 2.Finitely additive measures lack essential properties like continuity from below, making them unsuitable for probability in standard practice.
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    • 3.Dubins-Savage results apply narrowly to specific gambling contexts; they don't undermine countable additivity's role in general probability theory.
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    Related

    Continuous probability distributions require a restriction to countable additivi...Countable additivity is forced by topology and measure-theoretic limits, not mer...Dubins-Savage results apply narrowly to specific gambling contexts; they don't u...Dubins-Savage theory demonstrates gambling strategies viable under finitely addi...
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    Finitely additive measures lack essential properties like continuity from below,...Finitely additive measures on infinite spaces are mathematically consistent and ...Scientific practice often succeeds with non-countably-additive models, suggestin...

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