Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 209 / 5 / A2 / Segment

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- Solution Segment

Solution

On the segment the energy contains

c_{3} \int_{0}^{1} \int_{0}^{1} \frac{d s d t}{∣ s - t ∣},

which diverges logarithmically along the diagonal. The uniform segment measure therefore has infinite Green energy, so its mean cannot be defined as an

L^{2}

Gaussian-field pairing.

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