TY - JOUR AU - M. V. Pratsiovytyi PY - 1998/08/25 Y2 - 2024/03/28 TI - On finite convolutions of singular distributions and a “singular analog” of the Jessen-Wintner theorem JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 50 IS - 8 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/4857 AB - We study the fractal properties of a convolution of two Cantor distributions. By using the method of characteristic functions, we establish sufficient conditions for the singularity of the convolution of an arbitrary finite number of distributions of random variables with independent s-adic digits. We disprove the hypothesis on the validity of a “singular analog” of the Jessen-Wintner theorem for anomalously fractal distributions. ER -