Again the <series> converges absolutely. $T=2\sum_jB_j/3^j$ has the Cantor distribution. Every particular digit <sequence> has probability zero, so it has no atoms; its support is the Cantor set, which has Lebesgue measure zero, so it cannot have a Lebesgue density.

Solution

Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 4 / 26L / d / Solution

 Solution (source code)