Paper Info
Title
Finitistic and Frequentistic Approximation of Probability Measures with or without sigma-Additivity
Abstract
In this paper a theory of finitistic and frequentistic approxima- tions - in short: f-approximations - of probability measures P over a countably infinite outcome space N is developed. The family of subsets of N for which f-approximations converge to a (frequency) limit forms a pre-Dynkin system D }(N). The limiting probabil- ity measure over D can always be extended to a probability measure over }(N), but this measure is not always -additive. We conclude that probability measures can be regarded as idealizations of limiting frequencies if and only if -additivity is not assumed as a necessary axiom for probabilities. We prove that -additive probability mea- sures can be characterized in terms of canonical f-approximability, by means of conditioning to finite subsets of N. For non- -additive probability measures we achieve a result about semi-approximability. Our results generalize to rational-valued f-approximations. Finally, we transfer our results to probability measures on open or closed for-
Year
DOI
Venue
2008
10.1007/s11225-008-9128-3
Studia Logica
Keywords
DocType
Volume
frequency theory,probability,σ-additivity,finitistic approxi- mation.,finite additivity
Journal
89
Issue
Citations 
PageRank 
2
4
2.06
References 
Authors
4
2
Name
Order
Citations
PageRank
Gerhard Schurz111318.92
Hannes Leitgeb211519.26