Does anybody know of any derivation of Scotts general axiom (proven in zolton domotor's 1969 phd thesis), say within a probabilistic logic of some sort, which provides sufficient and necessary conditions for a strong numerical probabilistic representation even if the sample space is infinite.
This is the little known extension of Scotts results to infinite or perhaps atom-less sample space.s
Moreover, I am wondering whether it has been used in any kind of uniqueness representation proof (I presume the advantage of scotts infinite axiom is that it entails transitivity, and 'disjoint union' which otherwise have to proven directly using 'traditional structural sequence, monotone continuity, or archimedean axioms'. I presume that Scotts theorem still requires that almost equally probable events are equally probable (ie are events cannot differ in probability by an infinitesimal amount), as do archimedean axioms.
Is there any advantage of meetings its 'what appear to be' complicated conditions over and above say, an archimedean axiom, or monotone continuity
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