David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
We extend a result of Dubins  from bounded to unbounded random variables. Dubins  showed that a ﬁnitely additive expectation over the collection of bounded random variables can be written as an integral of conditional expectations (disintegrability) if and only if the marginal expectation is always within the smallest closed interval containing the conditional expectations (conglomerability). We give a suﬃcient condition to extend this result to the collection Z of all random variables that have ﬁnite expected value and whose conditional expectations are ﬁnite and have ﬁnite expected value. The suﬃcient condition also allows the result to extend some, but not all, subcollections of Z. We give an example where the equivalence of disintegrability and conglomerability fails for a subcollection of Z that still contains all bounded random variables.
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library||
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Peter Spirtes, A Polynomial Time Algorithm for Determining Dag Equivalence in the Presence of Latent Variables and Selection Bias.
Yeneng Sun (1996). Hyperfinite Law of Large Numbers. Bulletin of Symbolic Logic 2 (2):189-198.
Richard Bradley (2010). Proposition-Valued Random Variables as Information. Synthese 175 (1):17 - 38.
Stephen J. Montgomery-Smith & Alexander R. Pruss, A Comparison Inequality for Sums of Independent Random Variables.
Teddy Seidenfeld, Mark J. Schervish & Joseph B. Kadane, Preference for Equivalent Random Variables: A Price for Unbounded Utilities.
Philip G. Calabrese (2003). Operating on Functions with Variable Domains. Journal of Philosophical Logic 32 (1):1-18.
Added to index2009-01-28
Total downloads6 ( #196,681 of 1,096,603 )
Recent downloads (6 months)2 ( #158,594 of 1,096,603 )
How can I increase my downloads?