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    Home/Original/inverse
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    Inverse View

    It is not the case that 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).

    ?Set your confidence on the premises below to see your aggregate.

    Reasons For

    1 perspective
    Reason for
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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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    Reasons Against

    1 perspective
    Reason against
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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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