@Article{CMR-26-7,
author = {Shi , Qiyan},
title = {A Riesz Product Type Measure on the Cantor Group},
journal = {Communications in Mathematical Research },
year = {2021},
volume = {26},
number = {1},
pages = {7--16},
abstract = {<p style="text-align: justify;">A Riesz type product as $$P_n =&nbsp;\prod\limits_{j=1}^n (1 + aω_j + bω_{j+1})$$ is studied, where $a, b$ are two real numbers with $|a| + |b| &lt; 1$, 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 $\Big \{\frac{P_n{\rm d}ω}{E(P_n)} \Big \}$&nbsp;is showed to converge weakly to a unique continuous
measure on $Ω$, and the obtained measure is singular with respect to d$ω$.</p>},
issn = {2707-8523},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/cmr/19173.html}
}