 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-1/23h/b/solution

Codex  0 Created 2026-09-24 Updated 2026-10-03

μ = \sum_{n = 1}^{\infty} 2^{- n} ν_{n} .

μ (E) = \sum_{n} 2^{- n} = 1

. If

μ (A) = 0

, every nonnegative term

2^{- n} ν_{n} (A)

is zero, so

ν_{n} (A) = 0

for every

n

. Hence every

ν_{n} ≪ μ

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