منابع مشابه
Lexicographic probability, conditional probability, and nonstandard probability
The relationship between Popper spaces (conditional probability spaces that satisfy some regularity conditions), lexicographic probability systems (LPS’s) [Blume, Brandenburger, and Dekel 1991a; Blume, Brandenburger, and Dekel 1991b], and nonstandard probability spaces (NPS’s) is considered. If countable additivity is assumed, Popper spaces and a subclass of LPS’s are equivalent; without the as...
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Yalcin [23] shows that Kratzer’s model [5] does not validate some intuitively valid inferences and validates some intuitively invalid ones. He adopts a model based directly on a probability measure. However, as Kratzer [6] says, ‘Our semantic knowledge alone does not give us the precise quantitative notions of probability and desirability that mathematicians and scientists work with’, Yalcin’s ...
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The rst chapter presents Bayesian con rmation theory. We then construct in nitesimal numbers and use them to represent the probability of unrefuted hypotheses of standard probability zero. Popper's views on the nature of hypotheses, of probability and con rmation are criticised. It is shown that Popper conates total con rmation with weight of evidence. It is argued that Popper's corroboration c...
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Let (X, 3, v) be an internal measure space in a denumerably comprehensive enlargement. The set X is a standard measure space when equipped with the smallest standard o-algebra % containing the algebra a, where the extended real-valued measure p. on % is generated by the standard part of v. If / is fl-measurable, then its standard part / is jR-measurable on X. If / and p. are finite, then the vi...
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We prove the existence of optimal stopping points for upper semicontinuous two-parameter processes defined on filtered nonstandard (Loeb) probability spaces that satisfy a classical conditional independence hypothesis. The proof is obtained via a lifting theorem for elements of the convex set of randomized stopping points, which shows in particular that extremal elements of this set are ordinar...
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ژورنال
عنوان ژورنال: Notre Dame Journal of Formal Logic
سال: 1975
ISSN: 0029-4527
DOI: 10.1305/ndjfl/1093891802