# Convolutions of Cantor measures without resonance - Mathematics > Classical Analysis and ODEs

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Abstract: Denote by $\mu a$ the distribution of the random sum $1-a \sum {j=0}^\infty\omega j a^j$, where $P\omega j=0=P\omega j=1=1-2$ and all the choices areindependent. For $01$ and $\log 1-3-\log 1-4$ is irrational.

Autor: Fedor Nazarov, Yuval Peres, Pablo Shmerkin

Fuente: https://arxiv.org/