Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 129 / 4 / b / i

Table of contents
- Solution i

Solution

Repeated Cauchy-Schwarz inequality shows that the

U^{3}

norm dominates the absolute mean of a function:

∣ E f ∣ \leq ∥ f ∥_{U^{3}} .

Taking

f = 1_{A}

and using

E 1_{A} = α

gives

∥ 1_{A} ∥_{U^{3}} \geq α .

Solved by gpt-5.6-sol high.

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