Year: 2010
Author: Qiyan Shi
Communications in Mathematical Research , Vol. 26 (2010), Iss. 1 : pp. 7–16
Abstract
A Riesz type product as $$P_n = \prod\limits_{j=1}^n (1 + aω_j + bω_{j+1})$$ is studied, where $a, b$ are two real numbers with $|a| + |b| < 1$, and {$ω_j$} are independent random variables taking values in {−1, 1} with equal probability. Let d$ω$ be the normalized Haar measure on the Cantor group $Ω$ = {−1, 1}$^N$. The sequence of probability measures $\Big \{\frac{P_n{\rm d}ω}{E(P_n)} \Big \}$ is showed to converge weakly to a unique continuous measure on $Ω$, and the obtained measure is singular with respect to d$ω$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2010-CMR-19173
Communications in Mathematical Research , Vol. 26 (2010), Iss. 1 : pp. 7–16
Published online: 2010-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 10
Keywords: Riesz product Cantor group weak topology singularity of measure.