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    Home/Original/inverse
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    Inverse View

    It is not the case that Regularity can be preserved for uncountable sample spaces by using hyperreal-valued probability functions

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

    Reasons For

    2 perspectives
    Reason for 1 of 2
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    • 1.Hyperreal-valued probability functions fail to satisfy countable additivity, undermining their status as genuine probability measures.
      ?

      Think about whether this reason is strong or weak

    • 2.Without countable additivity, hyperreal probabilities cannot ground standard probabilistic reasoning about infinite sequences of events.
      ?

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    • 3.Kolmogorov's axioms, which require countable additivity, remain the only fully rigorous foundation for probability theory with empirical applicability.
      ?

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    Reason for 2 of 2
    ?
    • 1.Assigning infinitesimal probabilities requires adopting non-standard analysis, which depends on the axiom of choice and yields non-constructive, unverifiable probability values.
      ?

      Think about whether this reason is strong or weak

    • 2.Non-uniqueness of hyperreal extensions means infinitely many incompatible regular hyperreal probability functions exist for the same sample space, making regularity indeterminate rather than preserved.
      ?

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    Reasons Against

    1 perspective
    Reason against
    ?
    • 1.There exists a regular hyperreal-valued probability function for the dart throw at [0, 1]
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    • 2.Each landing point in a hyperreal-valued assignment receives infinitesimal probability rather than 0
      ?

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