On Convergence of a Sequence of Probability Measures on a Locally Compact Abelian Group to a Degenerate Limit

Authors

Teunis J. Ott

Document Type

Report

Publication Date

12-1-1975

Abstract

A condition is given on the Fourier-transforms of a sequence of probability measures on a locally compact abelian group G, which guarantees weak convergence of that sequence to a degenerate probability measure, and which is "weakest" with that property. The result is reformulated for the special case G = R^n, in which situation the Fourier-transforms are characteristic functions of n-dimensional random vectors.

Keywords

Operations research, Fourier transformations, Measure theory, Convergence, Random variables, Characteristic functions

Publication Title

Technical Memorandums from the Department of Operations, School of Management, Case Western Reserve University

Issue

Technical memorandum no. 371

Rights

This work is in the public domain and may be freely downloaded for personal or academic use

Recommended Citation

Ott, Teunis J., "On Convergence of a Sequence of Probability Measures on a Locally Compact Abelian Group to a Degenerate Limit" (1975). Research Reports from the Department of Operations. 351.
https://commons.case.edu/wsom-ops-reports/351