MEASURABLE GAMBLING HOUSES,

Abstract

It is shown in this paper that given a Borel measurability structure of the type used by Blackwell in dynamic programming, the utility of the house, while not necessarily Borel measurable, is absolutely measurable and hence its integral is defined with respect to any Borel measure. (A function is absolutely measurable if it is measurable with respect to the completion of the Borel sets under any measure.) Moreover, the gambler can do as well using only measurable policies (defined below) as he can using arbitrary policies.

Document Details

Document Type
Technical Report
Publication Date
Nov 01, 1965
Accession Number
AD0623459

Entities

People

  • Ralph E. Strauch

Organizations

  • RAND Corporation

Tags

DTIC Thesaurus Topics

  • Applied Mathematics
  • Computer Programming
  • Computing-Related Activities
  • Dynamic Programming
  • Gambling
  • Integrals
  • Interdisciplinary Science
  • Mathematical Analysis
  • Mathematical Programming
  • Mathematics
  • Measure Theory
  • Operations Research

Readers

  • Mathematical Modeling and Probability Theory.