Circularly invariant uniformizable probability measures for linear transformations

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Xu, Chuang¹ 

[1] Univ Alberta, Dept Math & Stat Sci, Edmonton, AB T6G 2G1, Canada

关键词: Circularly invariant uniformizable probability measure (CIUPM);    Uniformly distributed (modulo one) sequence;    Linear transformation;    Diameter;    Existence;    Uniqueness;   

DOI  :  10.1016/j.jmaa.2017.05.078

来源: Elsevier

【 摘 要 】

In this paper, we prove a threshold result on the existence of a circularly invariant uniformizable probability measure (CIUPM) for linear transformations with non-zero slope on the line. We show that there is a threshold constant c depending only on the slope of the linear transformation such that there exists a CIUPM if and only if its support has a diameter at least as large as c. Moreover, the CIUPM is unique up to translation if the diameter of the support equals c. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free