A Zero-one Law for a Class of Measures on Groups.

Abstract

Let (E beta) be a measurable (non-abelian) group, alpha a measurable homomorphism on E and mu a law on (E beta) satisfying mu = mu(alpha) v(alpha) (with mu(alpha) = mu o/alpha), for some law v(alpha) on (E beta). Under some additional conditions it is shown that, for every proper normal subgroup G of E and a in E, if Ga is an element of beta (mu), the mu-completion of B, then mu(Ga) = 0 or 1. As a corollary, it is shown that this result yields all previously known 0-1 laws for stable, semistable, and quasistable laws on linear spaces as well as new 0-1 laws for other classes of infinitely divisible laws on linear spaces.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Sep 01, 1979
Accession Number
ADA088374

Entities

People

  • Albert Tortrat
  • Balram Rajput
  • Donald Louie

Organizations

  • University of Tennessee

Tags

DTIC Thesaurus Topics

  • Algebra
  • Linear Algebra
  • Mathematical Analysis
  • Mathematics
  • Numerical Analysis
  • Permutations
  • Probability
  • Random Variables
  • Tennessee
  • Universities
  • Vector Spaces

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Mathematical Modeling and Probability Theory.

Technology Areas

  • Space