Countably additive full conditional probabilities

Author:

Armstrong Thomas E.

Abstract

Armstrong-Sudderth showed that a method of Carlson could be adapted to construct examples of countably additive full conditional probabilities. Here it is shown that all countably additive full conditional probabilities arise in this fashion. It is also shown that if the dimensionally ordered family of measures associated by Renyi to a full conditional probability contains an unbounded measure the full conditional probability fails to be countably additive. This leads to the notion of proper full conditional probabilities which if well founded in the sense of Krauss agree with the class of full conditional probabilities arising from Carlson’s construction. Section 3 explores the connection between coherence of countable betting systems and countable additivity of full conditional probabilities.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference15 articles.

1. When is the algebra of regular sets for a finitely additive Borel measure a 𝜎-algebra?;Armstrong, Thomas E.;J. Austral. Math. Soc. Ser. A,1982

2. 𝜅-finiteness and 𝜅-additivity of measures on sets and left invariant measures on discrete groups;Armstrong, Thomas E.;Proc. Amer. Math. Soc.,1980

3. Locally coherent rates of exchange;Armstrong, Thomas E.;Ann. Statist.,1989

4. A solution of Ulam’s problem on relative measure;Carlson, Tim;Proc. Amer. Math. Soc.,1985

5. B. deFinetti, Probability, induction, and statistics, Wiley, New York, 1972.

Cited by 5 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3