(untitled) (Communications in Mathematical Research, 2021)
A Riesz type product as P_n = _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 dω be the normalized Haar measure on the Cantor group Ω = −1, 1^N. The sequence of probability measures {P_ndωE(P_n) } is showed to converge weakly to a unique continuous measure on Ω, and the obtained measure is singular with respect to dω.