An Elementary Approach to the Daniell-Kolmogorov Theorem and Some Related Results.

Abstract

A short elementary proof is given of the Daniell Kolmogorov existence theorem for probability measures on product spaces, assuming nothing but the existence of Lebesgue measure on the unit interval. Related approaches are used to prove the existence of regular conditional distributions directly on Polish spaces, and to establish the existence of random measures and sets with given finite dimensional distributions or hitting probabilities, respectively. Keywords: Measures on product spaces; Regular conditional distributions; Random measures; Sets and point field; Finite dimensional distributions; Hitting probabilities.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1987
Accession Number
ADA186011

Entities

People

  • Olav Kallenberg

Organizations

  • University of North Carolina at Chapel Hill

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • 5G Wireless Networks
  • Computing-Related Activities
  • Construction
  • Convergence
  • Data Science
  • Diameters
  • Information Science
  • Intervals
  • North Carolina
  • Numbers
  • Probability
  • Random Variables
  • Real Numbers
  • Sequences
  • Statistics
  • Step Functions
  • Stochastic Processes

Fields of Study

  • Mathematics

Readers

  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space