Bernoulli convolutions: The dimension of Bernoulli convolutions

This lecture covers the concept of Bernoulli convolutions, focusing on the dimension of Bernoulli convolutions. It discusses the distribution of {±2", where I are i.i.d fair tosses, and explores the provided roots of a polynomial with specific coefficients. The lecture delves into folklore theorems and dimensional measures, self-similar means on R, and exact dimensional measures. It also touches upon the contraction factor, overlaps, and probe vectors in the context of Bernoulli convolutions.