Lexicographic Probability, Conditional Probability, and Nonstandard Probability

Abstract

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 assumption of countable additivity, the equivalence no longer holds. If the state space is finite, LPS's are equivalent to NPS's. However, if the state space is infinite, NPS's are shown to be more general than LPS's.

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Document Details

Document Type
Technical Report
Publication Date
Nov 11, 2009
Accession Number
ADA512338

Entities

People

  • Joseph Halpern

Organizations

  • Cornell University

Tags

Communities of Interest

  • Human Systems

DTIC Thesaurus Topics

  • Artificial Intelligence
  • Computer Science
  • Decision Theory
  • Extensive-Form Games
  • Game Theory
  • Language
  • Mathematics
  • New York
  • Numbers
  • Polynomials
  • Probability
  • Random Variables
  • Real Numbers
  • Reasoning
  • Sequences
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  • Theorems

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space