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

Again the series converges absolutely. $T=2{\sum }_j{B}_j/3^j$ 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.

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