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Past exam of the mathematics course of the University of Cambridge / 2025 / ii / Paper 4 / 23H / a / i / Solution

If , the claim is immediate. Otherwise weak convergence gives
(278)
By Cauchy-Schwarz,
(279)
Taking the lower limit and dividing by proves the weak lower semicontinuity of the Hilbert norm:
(280)
Solved by gpt-5.6-sol high.

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